Dendroidal sets

DOI10.2140/agt.2007.7.1441zbMath1133.55004arXivmath/0701293OpenAlexW3037628614WikidataQ58940926 ScholiaQ58940926MaRDI QIDQ2464800

Ittay Weiss, Ieke Moerdijk

Publication date: 17 December 2007

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701293

zbMATH Keywords

Kan complexoperadalgebras up to homotopyhomotopy coherent nerveweak \(n\)-categoriestensor product of operads

Mathematics Subject Classification ID

Related Items (62)

Homotopy theory of equivariant operads with fixed colors ⋮ \(\infty\)-operads via symmetric sequences ⋮ Quillen-Segal algebras and Stable homotopy theory ⋮ The homotopy theory of simplicial props ⋮ The configuration category of a product ⋮ An infinity operad of normalized cacti ⋮ Genuine equivariant operads ⋮ Moment categories and operads ⋮ Equivariant dendroidal Segal spaces and \(G\)-\(\infty\)-operads ⋮ 2-Segal spaces as invertible infinity-operads ⋮ Reedy categories which encode the notion of category actions ⋮ Algebraic weak factorisation systems. II: Categories of weak maps. ⋮ Modular operads and the nerve theorem ⋮ Equivariant dendroidal sets and simplicial operads ⋮ On autoequivalences of the \((\infty,1)\)-category of \(\infty\)-operads ⋮ Categories of graphs for operadic structures ⋮ Strictification theorems for the homotopy time-slice axiom ⋮ Free algebras through Day convolution ⋮ On rectification and enrichment of infinity properads ⋮ Group actions on Segal operads ⋮ On an extension of the notion of Reedy category ⋮ Truncated operads and simplicial spaces ⋮ A simplicial model for infinity properads ⋮ Configuration spaces form a Segal semi-dendroidal space ⋮ Operads of genus zero curves and the Grothendieck-Teichmüller group ⋮ Twisted arrow categories, operads and Segal conditions ⋮ Spaces of smooth embeddings and configuration categories ⋮ Graphical combinatorics and a distributive law for modular operads ⋮ Brane actions, categorifications of Gromov-Witten theory and quantum \(K\)-theory ⋮ From operator categories to higher operads ⋮ Equivariant dendroidal sets ⋮ Shuffles of trees ⋮ From homotopy operads to infinity-operads ⋮ An additivity theorem for the interchange of \(E_n\) structures ⋮ Higher cyclic operads ⋮ Dold-Kan correspondence for dendroidal Abelian groups ⋮ Operads and Phylogenetic Trees ⋮ Opetopic algebras I: Algebraic structures on opetopic sets ⋮ Fibered Multiderivators and (co)homological descent ⋮ Cubical model categories and quasi-categories ⋮ The incidence comodule bialgebra of the Baez-Dolan construction ⋮ Algebraic models for higher categories ⋮ \(C^\ast\)-algebraic drawings of dendroidal sets ⋮ Crossed simplicial group categorical nerves ⋮ Homotopy-coherent algebra via Segal conditions ⋮ Enriched \(\infty \)-operads ⋮ On the category of props ⋮ On inner Kan complexes in the category of dendroidal sets ⋮ Dendroidal spaces, \(\Gamma\)-spaces and the special Barratt-Priddy-Quillen theorem ⋮ A graphical category for higher modular operads ⋮ The dendroidal category is a test category ⋮ Feynman Graphs, and Nerve Theorem for Compact Symmetric Multicategories (Extended Abstract) ⋮ Morita homotopy theory for (\(\infty\),1)-categories and \(\infty\)-operads ⋮ A criterion for existence of right‐induced model structures ⋮ Dwyer–Kan homotopy theory for cyclic operads ⋮ Rational Pontryagin classes of Euclidean fiber bundles ⋮ Dendroidal sets as models for connective spectra ⋮ Algebraic K-Theory of ∞-Operads ⋮ Permutative categories, multicategories and algebraic \(K\)-theory ⋮ On the formality of the little disks operad in positive characteristic ⋮ Enriched \(\infty\)-categories via non-symmetric \(\infty\)-operads ⋮ On the homotopy theory of equivariant colored operads

Cites Work

• On inner Kan complexes in the category of dendroidal sets
• Tensor product of operads and iterated loop spaces
• The structure of autodistributive algebras
• Koszul duality for operads
• Category of \(A_\infty\)-categories
• Homotopy invariant algebraic structures on topological spaces
• Quasi-categories and Kan complexes
• The Boardman-Vogt resolution of operads in monoidal model categories
• The geometry of iterated loop spaces
• Vogt's theorem on categories of homotopy coherent diagrams
• Introduction to bicategories
• Higher Topos Theory (AM-170)
• On closed categories of functors
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