Simplicial homotopy theory
From MaRDI portal
Publication:5906407
zbMath0949.55001MaRDI QIDQ5906407
John F. Jardine, Paul G. Goerss
Publication date: 31 August 1999
Published in: Progress in Mathematics (Search for Journal in Brave)
localizationfibrationweak equivalencesimplicial setderived functorclosed model categorycofibrationPostnikov towerhomotopy coherence
Homotopy theory (55P99) Simplicial sets and complexes in algebraic topology (55U10) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Homotopy groups (55Q99) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology (55-01)
Related Items
A model for the homotopy theory of homotopy theory, Endotrivial modules for finite groups via homotopy theory, Higher stabilization and higher Freudenthal suspension, Quillen-Segal algebras and Stable homotopy theory, $\overline{Spec\mathbb Z}$ and the Gromov norm, The homotopy theory of simplicial props, Volume distortion in homotopy groups, The Seifert-van Kampen theorem and generalized free products of $S$-algebras, Cosimplicial DGLAs in Deformation Theory, Model category of diffeological spaces, Unnamed Item, A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type, Unnamed Item, The Moore Complex of a Simplicial Cocommutative Hopf Algebra, Computing All Maps into a Sphere, Theories of presheaf type, Cyclic multicategories, multivariable adjunctions and mates, On maps of a sphere to a simply connected space with finitely generated homotopy groups, Arakelov motivic cohomology II, A homotopy theory of coherently commutative monoidal quasi-categories, A closed model structure on the category of weakly unital dg categories, II, The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes, Unnamed Item, From simplicial homotopy to crossed module homotopy in modified categories of interest, Unnamed Item, On the third homology of 𝑆𝐿₂ and weak homotopy invariance, Principal bundles on two-dimensional CW-complexes with disconnected structure group, Model bicategories and their homotopy bicategories, Equivariant differential cohomology, Projective and Reedy model category structures for (infinitesimal) bimodules over an operad, Morita cohomology, Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting, Representing de Rham cohomology classes on an open Riemann surface by holomorphic forms, Limits and colimits, generators and relations of partial groups, Homotopy pro-nilpotent structured ring spectra and topological Quillen localization, Diagrams encoding group actions on Γ-spaces, On the telescopic homotopy theory of spaces, Brauer groups and étale cohomology in derived algebraic geometry, Are all localizing subcategories of stable homotopy categories coreflective?, Helly numbers of acyclic families, Unnamed Item, Catégorie homotopique stable d’un site suspendu avec intervalle, Higher Hochschild homology, topological chiral homology and factorization algebras, Mathematical models of abstract systems: knowing abstract geometric forms, On a possible application of the homotopy concept to model theory, Algebraic v. Topological K-Theory: A Friendly Match, The 1-type of a Waldhausen \(K\)-theory spectrum, Fibred sites and stack cohomology, Two-fold homotopy of 2-crossed module maps of commutative algebras, Unnamed Item, Rigidity and exotic models for the \(K\)-local stable homotopy category, Smoothness in Relative Geometry, Algebraic quantum kk-theory, Topological comparison theorems for Bredon motivic cohomology, The behaviour of the \(\overline{W}\)-construction on the homotopy theory of bisimplicial sets, From Γ-spaces to algebraic theories, Homotopical localizations of module spectra, W-types in homotopy type theory, A characterization of fibrant Segal categories, Streams, d-Spaces and Their Fundamental Categories, Joins of DGA modules and sectional category, Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings, Homotopy algebras and the inverse of the normalization functor, Complete Segal spaces arising from simplicial categories, The stable \(\mathbb{A}^1\)-connectivity theorems, The homotopy theory of fusion systems, Homotopy coherent centers versus centers of homotopy categories, \(v_*\)-torsion spaces and thick classes, Graded multiplications on iterated bar constructions, Braided injections and double loop spaces, Geometric models for higher Grothendieck-Witt groups in \(\mathbb A^1\)-homotopy theory, On relative and bi-relative algebraic 𝐾-theory of rings of finite characteristic, Topology and data, THE INTERSECTION MOTIVE OF THE MODULI STACK OF SHTUKAS, Higher Auslander algebras of type 𝔸 and the higher Waldhausen 𝖲-constructions, Towards non–abelian 𝑝–adic Hodge theory in the good reduction case, Quasirationality and prounipotent crossed modules, Contractible simplicial objects, MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES, The units of a ring spectrum and a logarithmic cohomology operation, Finite group actions on Kan complexes, Rational Cup Product and Algebraic K0-Groups of Rings of Continuous Functions, A Survey of (∞, 1)-Categories, Galois descent criteria, Functional Kan Simplicial Sets: Non-Constructivity of Exponentiation, On the classification of fibrations, A cocycle model for topological and Lie group cohomology, Chern–Weil forms and abstract homotopy theory, A model category structure on the category of simplicial categories, Nullification functors and the homotopy type of the classifying space for proper bundles, The logarithmic cotangent complex, On the de Rham cohomology of differential and algebraic stacks, Higher arithmetic \(K\)-theory, Extensions of $p$-local finite groups, Differential Geometry of Microlinear Frölicher Spaces IV-1, The two out of three property in ind-categories and a convenient model category of spaces, Splitting vector bundles outside the stable range and 𝔸¹-homotopy sheaves of punctured affine spaces, Cross effects and calculus in an unbased setting, HOMOTOPY MODEL THEORY, Unnamed Item, Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras, Secondary Hochschild cohomology., A model of type theory in simplicial sets. A brief introduction to Voevodsky's homotopy type theory, Integrating central extensions of Lie algebras via Lie 2-groups, On the third cohomology group of commutative monoids, Homotopy classification of gerbes, An overview of motivic homotopy theory, Nerves and classifying spaces for bicategories, Singular chains on topological stacks. I., Maurer-Cartan spaces of filtered \(L_{\infty}\)-algebras, A model structure à la Thomason on 2-Cat, Truncated resolution model structures, Towers and fibered products of model structures, On realizing diagrams of \(\Pi\)-algebras, The normaliser decomposition for \(p\)-local finite groups, Rigidification of algebras over multi-sorted theories, Diagrams and torsors, Operations on algebraic \(K\)-theory and regulators via the \(A^1\)-homotopy theory, Preorientations of the derived motivic multiplicative group, Comparison of models for \((\infty , n)\)-categories. I, Homotopy classification of braided graded categorical groups, A Thomason model structure on the category of small \(n\)-fold categories, The rational homology of spaces of long knots in codimension \(> 2\), Homology decompositions of the loops on 1-stunted Borel constructions of \(C_2\)-actions, A spectral sequence for Bredon cohomology, Spectral sequence operations converge to Araki-Kudo operations, Presenting higher stacks as simplicial schemes, \(F\)-isocrystals and homotopy types, Thomason cohomology of categories, Oka manifolds: from Oka to Stein and back, Trees of fusion systems, Lifting homotopy \(T\)-algebra maps to strict maps, Equivariant algebraic \(KK\)-theory and adjointness theorems, \(\mathbf{A}^1\)-homotopy theory of noncommutative motives, Homotopy homomorphisms and the classifying space functor, From double Lie groupoids to local Lie 2-groupoids, Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety, Survey article: an elementary illustrated introduction to simplicial sets, Higher cohomologies of modules, Simplicial descent categories, Automate parallèle à homotopie près. I. (Concurrent process up to homotopy. I), Abstract sectional category in model structures on topological spaces, Long knots and maps between operads, Delta-discrete \(G\)-spectra and iterated homotopy fixed points, The de Rham homotopy theory and differential graded category, Diagram spaces and symmetric spectra, Group actions on Segal operads, A homotopy theory for stacks, An algebraic model for finite loop spaces, Automorphisms of \(p\)-compact groups and their root data, On an extension of the notion of Reedy category, \(K\)-theory and the bridge from motives to noncommutative motives, On the loop space of a 2-category, Minimal fibrations and the organizing theorem of simplicial homotopy theory, Segal-type algebraic models of \(n\)-types, Homotopy colimits and global observables in abelian gauge theory, Existence and uniqueness of \(E_\infty\) structures on motivic \(K\)-theory spectra, Principal \(\infty\)-bundles: presentations, Nonabelian algebraic topology, CW towers and mapping spaces, Homotopy colimits of 2-functors, Étale homotopy types of moduli stacks of polarised abelian schemes, Refinements of the Chern-Dold character: cocycle additions in differential cohomology, Enriched categories and models for spaces of evolving states, Local-to-global spectral sequences for the cohomology of diagrams, Positive model structures for abstract symmetric spectra, Directional derivatives and higher order chain rules for abelian functor calculus, 2-Segal sets and the Waldhausen construction, Discrete \(G\)-spectra and embeddings of module spectra, Frobenius and the derived centers of algebraic theories, Equivariant simplicial cohomology with local coefficients and its classification, From homotopy operads to infinity-operads, A model categorical approach to group completion of \(E_n\)-algebras, Comparing cohomology obstructions, From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets, On Drinfeld's DG quotient, Double groupoids and homotopy 2-types, Central extensions of smooth 2-groups and a finite-dimensional string 2-group, Unifying derived deformation theories, Homotopical algebraic geometry. I: Topos theory, Fibrations of simplicial sets, Exact sequences and closed model categories, Models for the Maclaurin tower of a simplicial functor via a derived Yoneda embedding, Spherical posets from commuting elements, Crossed simplicial group categorical nerves, Homotopy theory of modules over operads in symmetric spectra, Webb's conjecture for fusion systems., 1-motivic sheaves and the Albanese functor, Model structures on the category of small double categories, Moduli stacks of algebraic structures and deformation theory, Comparing geometric realizations of tricategories, Homotopy colimits of classifying spaces of abelian subgroups of a finite group, Nerves of bicategories as stratified simplicial sets, Stable equivariant abelianization, its properties, and applications, Homotopy theory of spectral categories, The unit of the total décalage adjunction, The intrinsic formality of \(E_n\)-operads, Homotopy nilpotent groups, Bar constructions and Quillen homology of modules over operads, Generalized spectral categories, topological Hochschild homology and trace maps, STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS, Smooth Homotopy of Infinite-Dimensional 𝐶^{∞}-Manifolds, Perverse sheaves on Riemann surfaces as Milnor sheaves, Higher Structures in M‐Theory, ‐Algebras, the BV Formalism, and Classical Fields, Non-commutative derived moduli prestacks, Discrete differential calculus on simplicial complexes and constrained homology, Geometric Hodge filtered complex cobordism, Equivariant homotopy equivalence of homotopy colimits of \(G\)-functors, The Hurewicz theorem for cubical homology, Complete \(L_\infty \)-algebras and their homotopy theory, On the Goldman-Millson theorem for \(A_\infty\)-algebras in arbitrary characteristic, Smooth homotopy of diffeological spaces: theory and applications to infinite-dimensional 𝐶^{∞}-manifolds, Deligne-Riemann-Roch and intersection bundles, A monoidal Dold-Kan correspondence for comodules, The enriched Thomason model structure on 2-categories, On classifying simplicial modules, Rings and modules in Kan spectra, \(t\)-structures on stable derivators and Grothendieck hearts, Riemann-Roch for \(\overline{\operatorname{Spec}\mathbb{Z}}\), Unnamed Item, Invariants of a quadratic form attached to a tame covering of schemes., Taylor towers for \(\Gamma\)-modules, Every homotopy theory of simplicial algebras admits a proper model, The effective model structure and -groupoid objects, Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume, Higher fundamental groupoids for spaces, The abelianization of inverse limits of groups, Formal groups and stable homotopy of commutative rings, Derived Koszul duality and \(\mathsf{TQ}\)-homology completion of structured ring spectra, Basic constructions in rational homotopy theory of function spaces, \(\mathsf{TQ}\)-completion and the Taylor tower of the identity functor, Dold-Kan correspondence, revisited, Monoidal algebraic model structures, Operations in the homology spectral sequence of a cosimplicial infinite loop space, Enriched functor categories for functor calculus, Extensions of linking systems with \(p\)-group kernel, Bivariant Hermitian \(K\)-theory and Karoubi's fundamental theorem, 2-final 2-functors, Computations of relative topological coHochschild homology, Categorical, homological, and homotopical properties of algebraic objects, Another approach to the Kan-Quillen model structure, The loop-stable homotopy category of algebras, What is loop multiplication anyhow?, Geometric motives and the \(h\)-topology, On an enhancement of the category of shifted \(L_\infty\)-algebras, Nori diagrams and persistent homology, A Bousfield-Kan algorithm for computing the \textit{effective} homotopy of a space, Bousfield localisations along Quillen bifunctors, On the algebraic classification of module spectra, On \(\mathbb{A}^1\)-fundamental groups of isotropic reductive groups, Algebraic \(K\)-theory and descent for blow-ups, Universal bivariant algebraic \(K\)-theories, Galois actions on homotopy groups of algebraic varieties, Derived moduli of complexes and derived Grassmannians, Homotopy categories for simply connected torsion spaces, Group completion and units in \(\mathcal I\)-spaces, Cosimplicial models for the limit of the Goodwillie tower, A note on the equivariant Dold-Thom theorem, Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Homotopy colimits of algebras over Cat-operads and iterated loop spaces, Homotopical algebra for \(C^\ast\)-algebras, Fibre sequences and localization of simplicial sheaves, Homotopy completion and topological Quillen homology of structured ring spectra, Constructing derived moduli stacks, A universal characterization of higher algebraic \(K\)-theory, Polynomial-time homology for simplicial Eilenberg-MacLane spaces, Purity and homotopy theory of coalgebras, The homotopy groups of the simplicial mapping space between algebras, Massey products in differential cohomology via stacks, Homotopical decompositions of simplicial and Vietoris Rips complexes, Shuffles of trees, Homological epimorphisms, homotopy epimorphisms and acyclic maps, Homotopy theory of algebraic quantum field theories, Tracing cyclic homology pairings under twisting of graded algebras, Homotopy fiber products of homotopy theories, On the Grothendieck construction for \(\infty\)-categories, Rigidification of homotopy algebras over finite product sketches, Bicategorical homotopy fiber sequences, A combinatorial tool for computing the effective homotopy of iterated loop spaces, A note on the tangent bundle and Gauss functor of posets and manifolds, A Kripke model for simplicial sets, Yoneda lemma for complete Segal spaces, Codescent theory. I: Foundations, Combinatorial descent data for gerbes, The Frobenius condition, right properness, and uniform fibrations, Quasicategories of frames of cofibration categories, Weighted limits in simplicial homotopy theory, Homotopy theory of modules over operads and non-\(\varSigma \) operads in monoidal model categories, Differential graded versus simplicial categories, Cosimplicial resolutions and homotopy spectral sequences in model categories, Codimension two souls and cancellation phenomena, Simplicial structures in higher Auslander-Reiten theory, Comonad cohomology of track categories, Minimality in diagrams of simplicial sets, On Baer invariants of pairs of groups, On the twisted tensor product of small dg categories, Mapping spaces and \(R\)-completion, Gabriel-Zisman cohomology and spectral sequences, Subtle characteristic classes and Hermitian forms, Homotopy theory of monoids and derived localization, Right exact localizations of groups, Filter quotients and non-presentable \((\infty,1)\)-toposes, Maurer-Cartan moduli and theorems of Riemann-Hilbert type, Topological Quillen localization of structured ring spectra, Profinite spaces and problems of realizability, Equipping weak equivalences with algebraic structure, A graphical category for higher modular operads, Quasi-categories vs. Segal spaces: Cartesian edition, On the Maurer-Cartan simplicial set of a complete curved \(A_{\infty}\)-algebra, Morita homotopy theory for (\(\infty\),1)-categories and \(\infty\)-operads, Artin motives, weights, and motivic nearby sheaves, Computing simplicial representatives of homotopy group elements, Spectral sequences in \((\infty,1)\)-categories, On symmetric higher-dimensional automata and bisimilarity, A Cartan-Eilenberg spectral sequence for non-normal extensions, On Morita weak equivalences of simplicial algebraic theories and operads, Reedy diagrams in V-model categories, Geometric realization and its variants, Semitopologization in motivic homotopy theory and applications, Simplicial sets in topology, category theory, and beyond, Higher descent data as a homotopy limit, Model structures on the category of ex-spaces, Rigidification of algebras over essentially algebraic~theories, Homological localisation of model categories, On the Eilenberg-Zilber theorem for crossed complexes