Quasi-categories and Kan complexes

By André Joyal. 2002

381 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/2935c3eb92f9238fa0993139eab11fa590d0c410

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Citations in the corpus

The Character Theory of a Complex Group (2009, methodology): “tegory StC of stable C-linear ∞-categories (or equivalently, C-linear diﬀerential graded categories whose homotopy categories are triangulated). For foundations on ∞-categories (in the sense of Joyal [Jo]), we refer to the comprehensive work of Lurie [L1, L2]. (See Sections 2.1, 2.3, 2.2 for a summa”
Homotopy coherent adjunctions and the formal theory of monads (2013, positive): “The basic category theory of quasi-categories has been developed by Joyal [11,13,12], Lurie [18,19] (under the name ∞-categories), ourselves [23], and others.”
A Survey of (∞, 1)-Categories (2010, background): “Further details on quasi-categories can be found in Joyal’s papers [18] and [20].”
Decomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finiteness (2015, background): “By ∞-category we mean quasicategory in the sense of Joyal [18], [19], but follow rather the terminology of Lurie [28].”
Affineness and chromatic homotopy theory (2013, methodology): “Throughout this paper, we use the language of quasi-categories (that is,∞-categories) of [28, 33], and the theory of structured ring spectra as developed originally in [17], and formulated in ∞-categorical terms in [40].”
The 2-category theory of quasi-categories (2013, positive): “Join and slice Particularly to facilitate comparisons between our development of the theory of quasicategories, using the enriched category theories of 2-categories and simplicial categories, and the more traditional accounts following Joyal and Lurie, we review Joyal’s slice and join constructions,”
Units of ring spectra and Thom spectra (2008, background): “) is a quasicategory whenever C is, even for an arbitrary simplicial set X. An ∞-groupoid is an ∞-category with the property that its homotopy category is a groupoid (cf. [HTT, §1.2.5]); equivalently [Joy02], an ∞-category is a Kan complex, and so the homotopy category is the fundamental groupoid of”
A universal characterization of higher algebraic K-theory (2010, methodology): “l are Lurie’s books [52, 53]. We will write Cat∞ to denote the ∞-categoryof small ∞-categoriesand functors, which we explicitly model as the category of simplicial sets with the Joyal model structure [46]. There is a simplicial nerve functor N from simplicial categories to simplicial sets which is t”
Higher analytic stacks and GAGA theorems (2014, background): “ AND GAGA THEOREMS 3 higherstacksnotonlybecauseitismoregeneral,butalsobecauseitmakesmany constructionsandproofsclearerbothtechnicallyandconceptually. Ourapproachisbasedonthetheoryof∞-category(cf.Joyal[25]andLurie[32]). Ithasmanyadvantages. Inparticular,itenablesustocircumventtheclassical functoriali”
Enhanced six operations and base change theorem for higher Artin stacks (2012, neutral): “Joyal [21, 22] (where they are called quasi-categories), J.”
Algebraic weak factorisation systems I: Accessible AWFS☆ (2014, background): “Our final examples bear on the theory of quasicategories [32].”