A Survey of Graphical Languages for Monoidal Categories
From MaRDI portal
Publication:3000922
DOI10.1007/978-3-642-12821-9_4zbMath1217.18002arXiv0908.3347OpenAlexW3105507374WikidataQ59884671 ScholiaQ59884671MaRDI QIDQ3000922
Publication date: 31 May 2011
Published in: New Structures for Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0908.3347
monoidal categoriescoherencediagrammatic reasoningtraced categoriesgraphical languagesstring diagramscaveats
Related Items
A Categorical Reconstruction of Quantum Theory, A Finite Axiomatisation of Finite-State Automata Using String Diagrams, Concurrent Process Histories and Resource Transducers, Completeness of Nominal PROPs, A covariant Stinespring theorem, The spectrum of a localic semiring, String diagram rewrite theory II: Rewriting with symmetric monoidal structure, Quotient Categories and Phases, String Diagram Rewrite Theory I: Rewriting with Frobenius Structure, Causal inference via string diagram surgery, The geometry of Bayesian programming, On webs in quantum type C, Unnamed Item, A Graph Theoretic Perspective on CPM(Rel), Mermin Non-Locality in Abstract Process Theories, Categories of relations as models of quantum theory, An axiomatic approach to differentiation of polynomial circuits, Serre functors and graded categories, DisCoPy: Monoidal Categories in Python, From gs-monoidal to oplax cartesian categories: constructions and functorial completeness, Fundamental weight systems are quantum states, Combinatorial flows as bicolored atomic flows, Representations of fusion categories and their commutants, A Category of Surface-Embedded Graphs, Monoidal Width: Capturing Rank Width, String Diagrams for Layered Explanations, Monoidal categories, representation gap and cryptography, Protocol choice and iteration for the free cornering, Tensor networks in machine learning, Categorical foundations of gradient-based learning, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Categorical composable cryptography: extended version, Categorical composable cryptography, Bidirectional processes -- in category theory, physics, engineering, \dots, A diagrammatic view of differential equations in physics, Standard \(\lambda\)-lattices, rigid \(\mathrm{C}^\ast\) tensor categories, and (bi)modules, Microcanonical thermodynamics in general physical theories, Linear lambda terms as invariants of rooted trivalent maps, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Reversible monadic computing, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Interacting quantum observables: categorical algebra and diagrammatics, Unnamed Item, Unnamed Item, Categories of Differentiable Polynomial Circuits for Machine Learning, Graphical calculus of Hopf crossed modules, Shaded tangles for the design and verification of quantum circuits, A Note on an Old-Fashioned Algebra for (Disconnected) Graphs, Lawvere Categories as Composed PROPs, Unnamed Item, Unnamed Item, Generalised Mermin-type non-locality arguments, Biunitary constructions in quantum information, Unnamed Item, Unnamed Item, On Compositionality of Dinatural Transformations, Noncommutative network models, A channel-based perspective on conjugate priors, Unitary dual functors for unitary multitensor categories, Inversion, Iteration, and the Art of Dual Wielding, Disintegration and Bayesian inversion via string diagrams, Ribbon entwining datum, Quantum Mathematics in Artificial Intelligence, String diagram rewrite theory III: Confluence with and without Frobenius, Bicategorical semantics for nondeterministic computation, Bicommutant categories from fusion categories, A categorical foundation for structured reversible flowchart languages, High-level modelling for typed functional programming, Condition/decision duality and the internal logic of extensive restriction categories, Partial traces on additive categories, From reversible programming languages to reversible metalanguages, Interacting Hopf algebras, Bialgebras in Rel, A Graphical Foundation for Schedules, Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality, Pictures of complete positivity in arbitrary dimension, A mathematical theory of resources, Fusion categories via string diagrams, Dichromatic state sum models for four-manifolds from pivotal functors, Causal categories: relativistically interacting processes, Frobenius structures over Hilbert \(C^*\)-modules, Unnamed Item, Affinization of monoidal categories, Deligne’s category \underline{𝑅𝑒}𝑝(𝐺𝐿_{𝛿}) and representations of general linear supergroups, Tensor topology, A practical type theory for symmetric monoidal categories, Shadows and traces in bicategories, The categorified Heisenberg algebra. I: A combinatorial representation., The CBH characterisation theorem beyond algebraic quantum theory, A compositional approach to quantum functions, A Topological Perspective on Interacting Algebraic Theories, Operational axioms for diagonalizing states, Axiomatizing complete positivity, Towards Quantum Field Theory in Categorical Quantum Mechanics, Categorifying the ZX-calculus, Uniqueness of Composition in Quantum Theory and Linguistics, Executions in (Semi-)Integer Petri Nets are Compact Closed Categories, A finite-tame-wild trichotomy theorem for tensor diagrams, A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics, Traces in symmetric monoidal categories, Drags: a compositional algebraic framework for graph rewriting, Pivotal weak Turaev \(\pi \)-coalgebras, A graphical calculus for semi-groupal categories, Partially traced categories, The path relation for directed planar graphs in rectangles, and its relation to the free diad, Sheaf representation of monoidal categories, Relative Frobenius algebras are groupoids, Contextual equivalence for signal flow graphs, Coherence for closed categories with biproducts, Recoupling coefficients and quantum entropies, On representation categories of wreath products in non-integral rank, Blob homology, Unnamed Item, Towards a unified framework for decomposability of processes, Integral categories and calculus categories, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Petri nets are dioids: a new algebraic foundation for non-deterministic net theory, The Morita theory of quantum graph isomorphisms, Confluence of Graph Rewriting with Interfaces, A categorification of quantum \(\mathfrak{sl}_3\) projectors and the \(\mathfrak{sl}_3\) Reshetikhin-Turaev invariant of tangles, A graphical foundation for interleaving in game semantics, A string diagrammatic axiomatisation of finite-state automata, The structure of sum-over-paths, its consequences, and completeness for Clifford, Presentations of categories of modules using the Cautis-Kamnitzer-Morrison principle, Traces for coalgebraic components, Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks, A predicate/state transformer semantics for Bayesian learning, The algebra of partial equivalence relations, The symmetric tensor product on the Drinfeld centre of a symmetric fusion category, The transfer map of free loop spaces, Join inverse categories and reversible recursion, Categories of quantum and classical channels, On the geometry and algebra of networks with state, Perverse sheaves and knot contact homology, A new description of orthogonal bases, Universal Constructions for (Co)Relations: categories, monoidal categories, and props, A categorical foundation for structured reversible flowchart languages: Soundness and adequacy, Composing dinatural transformations: towards a calculus of substitution, The simplicial model of univalent foundations (after Voevodsky), The singular Temperley-Lieb category, The calculus of signal flow diagrams. I: Linear relations on streams., Modified traces for quasi-Hopf algebras, Join Inverse Categories as Models of Reversible Recursion, Bialgebraic foundations for the operational semantics of string diagrams, On higher holonomy invariants in higher gauge theory II, Exploring a Quantum Theory with Graph Rewriting and Computer Algebra, Differential categories revisited, Phase Groups and the Origin of Non-locality for Qubits, Graphical Calculus for Quantum Key Distribution (Extended Abstract), Monoidal characterisation of groupoids and connectors, Domain walls in topological phases and the Brauer-Picard ring for \(\mathrm{vec} (\mathbb{Z}/p\mathbb{Z})\), Computing fusion rules for spherical \(G\)-extensions of fusion categories, A Certified Study of a Reversible Programming Language, Unitary transformations of fibre functors, Dualizable tensor categories, Deligne categories in lattice models and quantum field theory, \textit{or} making sense of O(N) symmetry with non-integer N, Proof diagrams for multiplicative linear logic: syntax and semantics, The Mathematics of Text Structure
