Braided tensor categories
From MaRDI portal
Publication:1320266
DOI10.1006/aima.1993.1055zbMath0817.18007OpenAlexW2022595765WikidataQ55877599 ScholiaQ55877599MaRDI QIDQ1320266
Publication date: 23 July 1995
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aima.1993.1055
Related Items
Monoidal Grothendieck construction ⋮ The Right Braids, Quasi-braided Pre-tensor Categories, and General Yang–Baxter Operators ⋮ Classification of \(\mathfrak{sl}_3\) relations in the Witt group of nondegenerate braided fusion categories ⋮ Singular extensions and the second cohomology categorical group ⋮ Complete Iterativity for Algebras with Effects ⋮ On Braided Lie Structures of Algebras in the Categories of Weak Hopf Bimodules ⋮ Nilpotence, radicals and monoidal structures. With an appendix by Peter O'Sullivan. ⋮ Commutative algebras in Drinfeld categories of abelian Lie algebras ⋮ Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces ⋮ Homotopy classification of graded Picard categories ⋮ Homological epimorphisms, recollements and Hochschild cohomology -- with a conjecture by Snashall-Solberg in view ⋮ Bicategories for boundary conditions and for surface defects in 3-d TFT ⋮ Unnamed Item ⋮ Bialgebras in Rel ⋮ A Graphical Foundation for Schedules ⋮ A quantum double construction in Rel ⋮ A duality formalism in the spirit of Grothendieck and Verdier ⋮ WEAK BRAIDED BIALGEBRAS AND WEAK ENTWINING STRUCTURES ⋮ Discriminant algebras of finite rank algebras and quadratic trace modules ⋮ Symmetries and the u-condition in Hom-Yetter-Drinfeld categories ⋮ \(G\)-topological quantum field theory ⋮ Homological stability for automorphism groups ⋮ Integrable perturbations of conformal field theories and Yetter-Drinfeld modules ⋮ Wreaths, mixed wreaths and twisted coactions ⋮ Stable Postnikov data of Picard 2-categories ⋮ Symmetric pairs and pseudosymmetry of \(\Theta\)-Yetter-Drinfeld categories for Hom-Hopf algebras ⋮ \(N=2\) minimal conformal field theories and matrix bifactorisations of \(x^d\) ⋮ Universal Properties in Quantum Theory ⋮ Algebras versus coalgebras ⋮ Scalar extension of bicoalgebroids. ⋮ The fusion algebra of bimodule categories ⋮ The relative Deligne tensor product over pointed braided fusion categories ⋮ Pivotal structures of the Drinfeld center of a finite tensor category ⋮ Operads within monoidal pseudo algebras ⋮ Infinite loop spaces, and coherence for symmetric monoidal bicategories ⋮ \(\mathbb Z/2\mathbb Z\)-extensions of Hopf algebra module categories by their base categories ⋮ Comonadic base change for enriched categories ⋮ Webs of type Q ⋮ Relative centers and tensor products of tensor and braided fusion categories ⋮ Coherence for invertible objects and multigraded homotopy rings ⋮ ON MATRIX QUANTUM GROUPS OF TYPE An ⋮ Triangulations, orientals, and skew monoidal categories ⋮ Formal plethories ⋮ Group cohomology and gauge equivalence of some twisted quantum doubles ⋮ Elliptic associators ⋮ Yetter-Drinfeld modules over weak braided Hopf monoids and center categories ⋮ Platonic and alternatinc 2-groups ⋮ A short survey on observability ⋮ The 1-type of a Waldhausen \(K\)-theory spectrum ⋮ EXPLICIT cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf–Witten invariants ⋮ The Eckmann-Hilton argument and higher operads ⋮ Generalization of braids and homologies ⋮ Galois Action on Knots II: Proalgebraic String Links and Knots ⋮ Classification of braids which give rise to interchange ⋮ Quadratic algebra of square groups ⋮ DOUBLE BICROSSPRODUCTS IN BRAIDED TENSOR CATEGORIES ⋮ Cardy algebras and sewing constraints. II ⋮ Revisiting the categorical interpretation of dependent type theory ⋮ A skew-duoidal Eckmann-Hilton argument and quantum categories ⋮ Blocked-braid groups ⋮ Bicategorical homotopy fiber sequences ⋮ The pivotal cover and Frobenius-Schur indicators ⋮ Equivariant extensions of categorical groups ⋮ Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups. ⋮ Conformal orbifold theories and braided crossed \(G\)-categories ⋮ Weak \(C\)-cleft extensions and weak Galois extensions. ⋮ Hopf Algebras ⋮ Braids, their Properties and Generalizations ⋮ Weak tensor category and related generalized Hopf algebras. ⋮ Braided injections and double loop spaces ⋮ Quantum field theory on curved spacetimes: Axiomatic framework and examples ⋮ ON THE BRAIDING OF AN ANN-CATEGORY ⋮ Braided distributivity ⋮ On a symmetry of Müger's centralizer for the Drinfeld double of a semisimple Hopf algebra. ⋮ Building vertex algebras from parts ⋮ Rank-finiteness for modular categories ⋮ On the Brauer-Picard group of a finite symmetric tensor category ⋮ Monoidal Indeterminates and Categories of Possible Worlds ⋮ Dynamical systems and sheaves ⋮ A Classical Propositional Logic for Reasoning About Reversible Logic Circuits ⋮ The diagram category of framed tangles and invariants of quantized symplectic group ⋮ The braided monoidal structures on the category of vector spaces graded by the Klein group ⋮ An Australian Conspectus of Higher Categories ⋮ A note on the biadjunction between 2-categories of traced monoidal categories and tortile monoidal categories ⋮ A topological origin of quantum symmetric pairs ⋮ Hom-Tensor categories and the Hom-Yang-Baxter Equation ⋮ Traces in monoidal categories ⋮ Induction, Coinduction, and Adjoints ⋮ dg analogues of the Zuckerman functors and the dual Zuckerman functors. I ⋮ On sovereign, balanced and ribbon quasi-Hopf algebras ⋮ CATEGORICAL ASPECTS OF VIRTUALITY AND SELF-DISTRIBUTIVITY ⋮ Quantum group constructions in a symmetric monoidal category ⋮ Double braidings, twists and tangle invariants ⋮ Monoidal functors, graphs, and field algebras ⋮ Infinitesimal 2-braidings and differential crossed modules ⋮ AN ALGEBRAIC APPROACH TO SYMMETRIC PRE-MONOIDAL STATISTICS ⋮ Braided Drinfeld and Heisenberg doubles. ⋮ An alternative description of braided monoidal categories ⋮ THE CENTER OF THE CATEGORY OF BIMODULES AND DESCENT DATA FOR NONCOMMUTATIVE RINGS ⋮ Localization of Monoid Objects and Hochschild Homology ⋮ On the classification of strongly graded Hopf algebras ⋮ Monoidal structure of the category of \(u^+_q\)-modules. ⋮ Factorization problems on rational loop groups, and the Poisson geometry of Yang-Baxter maps ⋮ Yetter-Drinfeld modules for crossed structures. ⋮ Braided premonoidal Mac Lane coherence ⋮ The symplectic fermion ribbon quasi-Hopf algebra and the \(S L(2, \mathbb{Z})\)-action on its centre ⋮ Hopf Galois extensions, triangular structures, and Frobenius Lie algebras in prime characteris\-tic. ⋮ Galois extensions of braided tensor categories and braided crossed G-categories ⋮ Double construction for crossed Hopf coalgebras. ⋮ The Hom-Long dimodule category and nonlinear equations ⋮ Enrichment over iterated monoidal categories ⋮ Braids and linear algebra ⋮ Paracategories. II: Adjunctions, fibrations and examples from probabilistic automata theory ⋮ Factorizable quasi-Hopf algebras -- applications. ⋮ On the Frobenius-Schur indicators for quasi-Hopf algebras. ⋮ Tangles and Hopf algebras in braided categories ⋮ Higher categories, strings, cubes and simplex equations ⋮ Toward a Galois theory of the integers over the sphere spectrum ⋮ Coherence via focusing for symmetric skew monoidal categories ⋮ Double construction for monoidal categories ⋮ Monoidal bicategories and Hopf algebroids ⋮ Hecke modules from metaplectic ice ⋮ Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures ⋮ Quantum commutative algebras and their duals ⋮ Pathlike co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics ⋮ Higher-dimensional algebra. II: 2-Hilbert spaces ⋮ A theory of tensor products for module categories for a vertex operator algebra. I ⋮ Higher cohomologies of commutative monoids ⋮ Crossed modules, quantum braided groups, and ribbon structures ⋮ Reconstruction in braided categories and a notion of commutative bialgebra ⋮ Tensor products and discriminants of unital quadratic forms over commutative rings ⋮ The development and prospects for category theory ⋮ Combinatorial Hopf algebras and towers of algebras -- dimension, quantization and functorality. ⋮ Drinfeld center of enriched monoidal categories ⋮ String diagrams for traced and compact categories are oriented 1-cobordisms ⋮ Monoidal functors on the category of representations of a triangular Hopf algebra ⋮ A Tannakian context for Galois theory ⋮ Simple free star-autonomous categories and full coherence ⋮ Idempotents and one-sided units: lattice invariants and a semigroup of functors on the category of monoids ⋮ Center construction and duality of category of Hom-Yetter-Drinfeld modules over monoidal Hom-Hopf algebras ⋮ Iterated monoidal categories ⋮ On the structure of the Witt group of braided fusion categories ⋮ Self-adjunctions and matrices. ⋮ On Hopf adjunctions, Hopf monads and Frobenius-type properties ⋮ On the second fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Hecke algebras, finite general linear groups, and Heisenberg categorification. ⋮ Monoidal structures on the categories of quadratic data ⋮ Actions of monoidal categories and generalized Hopf smash products. ⋮ A Larson-Sweedler theorem for Hopf \(\mathcal{V} \)-categories ⋮ \(\pi\)-twist and orientability in braided categories. ⋮ A class of prime fusion categories of dimension \(2^N\) ⋮ Quasi-quantum groups as internal symmetries of topological quantum field theories ⋮ Enriched duality in double categories: \(\mathcal{V}\)-categories and \(\mathcal{V}\)-cocategories ⋮ Groups up to congruence relation and from categorical groups to c-crossed modules ⋮ Chord diagram invariants of tangles and graphs ⋮ Braided groups and algebraic quantum field theories ⋮ Galois theory for braided tensor categories and the modular closure ⋮ The symmetric tensor product on the Drinfeld centre of a symmetric fusion category ⋮ Quantum invariants of knotoids ⋮ Flags and tangles ⋮ The 2-dimensional stable homotopy hypothesis ⋮ Hypergraph categories ⋮ Cohomology of monoids with operators ⋮ Multiplication alteration by two-cocycles: the non-associative version ⋮ Weak \(C\)-cleft extensions, weak entwining structures and weak Hopf algebras. ⋮ Ribbon transformations, integrals, and triangular decompositions. ⋮ Symmetric bimonoidal intermuting categories and \(\omega\times\omega\) reduced bar constructions ⋮ Cohomological classification of braided Ann-categories ⋮ Quasi-quantum groups obtained from tensor braided Hopf algebras ⋮ Coherence of associativity in categories with multiplication ⋮ The groupoid of finite sets is biinitial in the 2-category of rig categories ⋮ The \(n\)-fold reduced bar construction ⋮ Circuit algebras are wheeled props ⋮ Reflection fusion categories ⋮ Braided Picard groups and graded extensions of braided tensor categories ⋮ Skew braces as remnants of co-quasitriangular Hopf algebras in suplat ⋮ Categories of pairings ⋮ The Brauer group of a braided monoidal category ⋮ Generalized centers of braided and sylleptic monoidal 2-categories ⋮ Monoidal globular categories as a natural environment for the theory of weak \(n\)-categories ⋮ Quinn's formula and abelian 3-cocycles for quadratic forms ⋮ Braided bosonization and inhomogeneous quantum groups ⋮ Boundary topological entanglement entropy in two and three dimensions ⋮ Representable multicategories ⋮ The quantum double and related constructions ⋮ On the homotopy structure of strongly homotopy associative algebras ⋮ Finite Hopf algebras in braided tensor categories ⋮ Symmetric centres of braided monoidal categories ⋮ The symmetry enriched center functor is fully faithful ⋮ The braidings of mapping class groups and loop spaces ⋮ Categories of representations of coalgebroids ⋮ Computing the group of minimal non-degenerate extensions of a super-Tannakian category ⋮ A Picard-Brauer exact sequence of categorical groups ⋮ Cross product bialgebras. I ⋮ Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group ⋮ On the categorical structure of \(H^{2}\) ⋮ Tortile tensor categories ⋮ From subfactors to categories and topology. I: Frobenius algebras in and Morita equivalence of tensor categories ⋮ Abstract substitution in enriched categories ⋮ Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras ⋮ Braided equivariant crossed modules and cohomology of \(\gamma\)-modules ⋮ Bar categories and star operations ⋮ On Müger's centralizer in braided equivariantized fusion categories ⋮ Classification of metaplectic modular categories ⋮ On the third cohomology group of commutative monoids ⋮ Generalized braided Hopf algebras. ⋮ Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension. ⋮ Pseudosymmetric braidings, twines and twisted algebras. ⋮ Nerves and classifying spaces for bicategories ⋮ Pictures of complete positivity in arbitrary dimension ⋮ On an analogue of a Brauer theorem for fusion categories ⋮ The sovereign structure on categories of entwined modules ⋮ Quantum group-twisted tensor products of \(C^*\)-algebras. II. ⋮ Connected braided Hopf algebras. ⋮ A characterization of weak Hopf (co) quasigroups ⋮ Tetramodules over a bialgebra form a 2-fold monoidal category ⋮ Homotopy classification of braided graded categorical groups ⋮ On the cobordism and commutative monoid with cancellation approaches to conformal field theory ⋮ TFT construction of RCFT correlators. III: Simple currents ⋮ Two-dimensional monad theory ⋮ Structure and classification of monoidal groupoids ⋮ Frobenius-Schur indicators and exponents of spherical categories. ⋮ Shadows and traces in bicategories ⋮ General twisting of algebras. ⋮ Medial commutativity ⋮ Classifying spaces for braided monoidal categories and lax diagrams of bicategories ⋮ Lie algebras in symmetric monoidal categories ⋮ Functoriality of the center of an algebra ⋮ Monoidal 2-structure of bimodule categories ⋮ Tate motives and the periodicity operators of Connes ⋮ Traces in symmetric monoidal categories ⋮ Some results on strict graded categorical groups ⋮ Additive closed symmetric monoidal structures on \(R\)-modules ⋮ Commutativity ⋮ Monoidal indeterminates and categories of possible worlds ⋮ Non-canonical isomorphisms ⋮ A cohomology theory for commutative monoids. ⋮ Intermutation ⋮ Higher cohomologies of modules ⋮ Associahedra and weak monoidal structures on categories ⋮ Milnor-Moore categories and monadic decomposition ⋮ Differential graded categories and Deligne conjecture ⋮ Loop spaces, and coherence for monoidal and braided monoidal bicategories ⋮ Topological boundary conditions in abelian Chern-Simons theory ⋮ Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations ⋮ Duals invert ⋮ From Atiyah classes to homotopy Leibniz algebras ⋮ Weighted tensor products of Joyal species, graphs, and charades ⋮ Hopf comonads on naturally Frobenius map-monoidales ⋮ Centers and homotopy centers in enriched monoidal categories ⋮ Pseudo-commutativity of KZ 2-monads ⋮ A Clifford algebra is a weak Hopf algebra in a suitable symmetric monoidal category. ⋮ The braided monoidal structures on a class of linear Gr-categories ⋮ Duality, crossing and MacLane's coherence ⋮ A graphical foundation for interleaving in game semantics ⋮ Laplaza sets, or how to select coherence diagrams for pseudo algebras ⋮ Not every pseudoalgebra is equivalent to a strict one ⋮ Projections and Yetter-Drinfel'd modules over Hopf (co)quasigroups ⋮ Intercategories: a framework for three-dimensional category theory ⋮ Operad groups and their finiteness properties ⋮ Coherence and strictification for self-similarity ⋮ Refinements of the Chern-Dold character: cocycle additions in differential cohomology ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Weak Hopf algebras and weak Yang-Baxter operators. ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ Morita classes of algebras in modular tensor categories ⋮ Categories of quantum and classical channels ⋮ On the geometry and algebra of networks with state ⋮ Perverse sheaves and knot contact homology ⋮ Cardy algebras and sewing constraints. I ⋮ Modular invariants for group-theoretical modular data. I ⋮ A sequence to compute the Brauer group of certain quasi-triangular Hopf algebras. ⋮ Limits and colimits of Hopf algebras ⋮ Central extensions of smooth 2-groups and a finite-dimensional string 2-group ⋮ On algebraic K-theory categorical groups ⋮ Projections of weak braided Hopf algebras. ⋮ An abstract characterization of Thompson's group \(F\). ⋮ Pentagon and hexagon equations ⋮ On braided fusion categories. I ⋮ Commutative algebras in Fibonacci categories ⋮ Centre of an algebra ⋮ Constructing new braided \(T\)-categories over weak Hopf algebras. ⋮ Butterflies. II: Torsors for 2-group stacks ⋮ Monads on higher monoidal categories ⋮ On gauging symmetry of modular categories ⋮ Braided doubles and rational Cherednik algebras. ⋮ Comparing geometric realizations of tricategories ⋮ Nerves of bicategories as stratified simplicial sets ⋮ On the inverse braid monoid. ⋮ Yetter-Drinfeld categories associated with a weak braided Hopf algebra. ⋮ Braided bialgebras of Hecke-type. ⋮ The Brauer category and invariant theory ⋮ Butterflies. I: Morphisms of 2-group stacks ⋮ Formal Hopf algebra theory. II: Lax centres ⋮ Dendriform algebras relative to a semigroup ⋮ The weak braided Hopf algebra structure of some Cayley-Dickson algebras ⋮ Rank of quantized universal enveloping algebras and modular functions ⋮ Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics ⋮ Exact sequences, Hochschild cohomology, and the Lie module structure over the \(M\)-relative center ⋮ Triviality theorems for Yetter-Drinfel'd Hopf algebras. ⋮ Cohomology of finite tensor categories: Duality and Drinfeld centers ⋮ Feedback, trace and fixed-point semantics ⋮ Braided skew monoidal categories ⋮ Orders and dimensions for sl(2) or sl(3) module categories and boundary conformal field theories on a torus ⋮ Hopf modules and the double of a quasi-Hopf algebra ⋮ ON THE GENERALIZED H-LIE STRUCTURE OF ASSOCIATIVE ALGEBRAS IN YETTER-DRINFELD CATEGORIES ⋮ Unnamed Item ⋮ Quantum and braided ZX calculus* ⋮ CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES ⋮ Quantum determinants in ribbon category ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The Monoidal Category of Yetter-Drinfeld Modules over a Weak Braided Hopf Algebra ⋮ Slightly Degenerate Categories and ℤ-Modular Data ⋮ Coherence for bicategorical cartesian closed structure ⋮ Weak units, universal cells, and coherence via universality for bicategories ⋮ Cofree objects in the centralizer and the center categories ⋮ The Brauer–Picard groups of fusion categories coming from the ADE subfactors ⋮ On the definition and K-theory realization of a modular functor ⋮ Recoupling Lie algebra and universal ω-algebra ⋮ Braiding for categorical algebras and crossed modules of algebras II: Leibniz algebras ⋮ Analysis on superspace: an overview ⋮ Unnamed Item ⋮ Higher cohomologies for presheaves of commutative monoids ⋮ Linear Exponential Comonads without Symmetry ⋮ Logarithmic conformal field theory, log-modular tensor categories and modular forms ⋮ A quasi-Hopf algebra for the triplet vertex operator algebra ⋮ Pointed finite tensor categories over abelian groups ⋮ Symmetry and pseudosymmetry of v-Yetter–Drinfeld categories for Hom–Hopf algebras ⋮ Unnamed Item ⋮ New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras ⋮ A GNS construction of three-dimensional abelian Dijkgraaf–Witten theories ⋮ Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology ⋮ Oplax Hopf Algebras ⋮ Coherence for bicategories, lax functors, and shadows ⋮ Higher-dimensional algebra and topological quantum field theory ⋮ Manin products, Koszul duality, Loday algebras and Deligne conjecture ⋮ Traced monoidal categories ⋮ A remark about the anomalies of cyclic holomorphic permutation orbifolds ⋮ Some exact sequences associated with adjunctions in bicategories. Applications ⋮ Braiding for categorical algebras and crossed modules of algebras I: Associative and Lie algebras ⋮ Interacting quantum observables: categorical algebra and diagrammatics ⋮ Witness algebra and anyon braiding ⋮ Unnamed Item ⋮ Buildings, spiders, and geometric Satake ⋮ The classifying space of a categorical crossed module ⋮ Unnamed Item ⋮ Symmetries and theu-condition in weak monoidal Hom–Yetter–Drinfeld categories ⋮ Representation stability for pure braid group Milnor fibers ⋮ Centre of Monoids, Centralisers, and Localisation ⋮ Quantized braided linear algebras relating to quantized braided groups ⋮ Graphical calculus of Hopf crossed modules ⋮ Coherence in monoidal track categories ⋮ Generalized double crossproducts associated with the quantized enveloping algebras ⋮ A Compositional Framework for Passive Linear Networks ⋮ On homological properties of singular braids ⋮ Compact quantum groups associated with monoidal functors ⋮ Drinfeld Double for Braided Infinitesimal Hopf Algebras ⋮ FOCK REPRESENTATIONS AND QUANTUM MATRICES ⋮ Topological field theory on r-spin surfaces and the Arf-invariant ⋮ Radford's biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras ⋮ Quantum Speedup and Categorical Distributivity ⋮ Dialogue Categories and Frobenius Monoids ⋮ Adjunctions and braided objects ⋮ MORE EXAMPLES OF PSEUDOSYMMETRIC BRAIDED CATEGORIES ⋮ Compact quantum groups and their corepresentations ⋮ Symmetric monoidal categories and $\Gamma$-categories ⋮ The algebra of strand splitting. I. A braided version of Thompson's group V ⋮ Quantum traces and quantum dimensions for quasi-Hopf algebras ⋮ Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings ⋮ Hochschild Homology in a Braided Tensor Category ⋮ Quasitriangular Structures for a Class of Hopf Algebras of Dimensionp6 ⋮ Unnamed Item ⋮ Tresses et structure entière sur la catégorie des représentations de slNquantique ⋮ Extensions of tensor categories by finite group fusion categories ⋮ Characterization of quasi-Yetter–Drinfeld modules ⋮ Unnamed Item ⋮ On traced monoidal closed categories ⋮ Mathematics of topological quantum computing ⋮ Vector product and composition algebras in braided monoidal additive categories ⋮ Noncommutative network models ⋮ Compatibility Conditions Between Rings and Corings ⋮ Unnamed Item ⋮ Covering groups of nonconnected topological groups and 2-groups ⋮ HOMOTOPY QUANTUM FIELD THEORIES AND THE HOMOTOPY COBORDISM CATEGORY IN DIMENSION 1 + 1 ⋮ Quantum Invariants of Templates ⋮ Pointed braided tensor categories ⋮ Two theorems on balanced braces ⋮ The Next Step Beyond Graded Lie Algebra: Recoupling Lie Algebra ⋮ Unnamed Item ⋮ Extended TQFTs via generators and relations I: The extended toric code ⋮ Cleft extensions in braided categories ⋮ Relative Yetter-Drinfeld modules and comodules over braided groups ⋮ Finite quasi-quantum groups of rank two ⋮ The Hom–Yang–Baxter equation and Hom–Lie algebras ⋮ Dyslexia and duals of hopf algebras in braided monoidal categories ⋮ Yetter–Drinfel’d modules over weak Hopf quasigroups ⋮ Braided yang-baxter operators ⋮ Symmetric pairs and pseudosymmetries in Hom-Yetter–Drinfeld categories ⋮ Pseudotriangular weak Hopf algebras ⋮ Mixed Witt rings of algebras with involution ⋮ Completeness of Nominal PROPs ⋮ Congruence Lattices of Ideals in Categories and (Partial) Semigroups ⋮ Composing PROBs ⋮ Unnamed Item ⋮ Non-simple quasitriangular Hopf algebras of dimension \(pq^2\) ⋮ Reconstructing braided subcategories of \(SU (N)_k \) ⋮ Minimal nondegenerate extensions ⋮ Simple transitive 2‐representations of Soergel bimodules for finite Coxeter types ⋮ Irrational braided generalized near-groups ⋮ The boundary phase transitions of the 2+1D \(\mathbb{Z}_N\) topological order via topological Wick rotation ⋮ On relations among quadratic modules ⋮ Differential graded vertex operator algebras and their Poisson algebras ⋮ IntroSurvey of representation theory ⋮ When does a three-dimensional Chern-Simons-Witten theory have a time reversal symmetry? ⋮ Davydov-Yetter cohomology and relative homological algebra ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Understanding the small object argument ⋮ PURE-BRAIDED HOPF ALGEBRAS AND KNOT INVARIANTS ⋮ Understanding the small object argument ⋮ AN ANALOGUE OF KEGEL'S THEOREM FOR QUASI-ASSOCIATIVE ALGEBRAS ⋮ On the equality of \(q\)-dimension and intrinsic dimension ⋮ Crossed Burnside rings. I: The fundamental theorem ⋮ Cosovereign Hopf algebras ⋮ Cross product bialgebras. II ⋮ Categorical \(G\)-crossed modules and 2-fold extensions ⋮ Two applications of analytic functors ⋮ Tannaka duality for Maschkean categories ⋮ Higher-dimensional Mac Lane's pentagon and Zamolodchikov equations ⋮ Schrödinger representations from the viewpoint of tensor categories. ⋮ Quasi-quantum linear spaces. ⋮ A Categorical Approach to Turaev's Hopf Group-Coalgebras ⋮ Universal central extensions of braided crossed modules of Lie algebras ⋮ In and around abelian anyon models * ⋮ Braided Frobenius algebras from certain Hopf algebras ⋮ Invertible skew pairings and crossed products for weak Hopf algebras ⋮ Toward the group completion of the Burau representation ⋮ On symmetric representations of 𝑆𝐿₂(ℤ)