Homotopy coherent category theory and \(A_\infty\)-structures in monoidal categories

DOI10.1016/S0022-4049(96)00084-9zbMath0892.18003MaRDI QIDQ1380029

Mikhail A. Batanin

Publication date: 3 August 1998

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

category of diagramshomotopy coherent diagramslocally Kan simplicialsimplicial \(A_\infty\)-graphsimplicially enriched category

Mathematics Subject Classification ID

Abstract and axiomatic homotopy theory in algebraic topology (55U35) Graphs, diagram schemes, precategories (18A10) Enriched categories (over closed or monoidal categories) (18D20)

Related Items (20)

Higher stabilization and higher Freudenthal suspension ⋮ Derived Koszul duality and \(\mathsf{TQ}\)-homology completion of structured ring spectra ⋮ Symmetrisation of \(n\)-operads and compactification of real configuration spaces ⋮ Correction to: ``Homotopy theory of nonsymmetric operads. I--II ⋮ Homotopy theory of non-symmetric operads. II: Change of base category and left properness ⋮ Formal aspects of Gray's tensor products of 2-categories ⋮ The twisted tensor product of \(\operatorname{dg}\) categories and a contractible 2-operad ⋮ Cofibrant operads and universal \(E_{\infty}\) operads. ⋮ $(A_\infty,2)$-categories and relative 2-operads ⋮ Variations on a theme of homotopy ⋮ A classification of Taylor towers of functors of spaces and spectra ⋮ The Eckmann-Hilton argument and higher operads ⋮ Homotopy theory of nonsymmetric operads ⋮ Homotopy theory of modules over operads and non-\(\varSigma \) operads in monoidal model categories ⋮ Operads and PROPs ⋮ On the twisted tensor product of small dg categories ⋮ Monoidal globular categories as a natural environment for the theory of weak \(n\)-categories ⋮ Unnamed Item ⋮ The universal property of the multitude of trees ⋮ Dwyer-Kan homotopy theory of enriched categories

Cites Work

• Uniqueness of delooping machines
• Bar and cobar constructions. I
• Koszul duality for operads
• Homotopy limits and colimits
• Homotopy invariant algebraic structures on topological spaces
• A convenient category of topological spaces
• Homotopical algebra
• The geometry of iterated loop spaces
• Homotopy limits, completions and localizations
• Vogt's theorem on categories of homotopy coherent diagrams
• HOMOTOPY THEORY OF COALGEBRAS
• A Note on Homotopy Equivalences
• Homotopy coherent category theory
• Homotopy Associativity of H-Spaces. I
• On the van Kampen theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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