Skip to content
EntityQ7269442· pop 7· linked from 151 articles

quasi-category

Sign in to save

Also known as quasicategory, (∞,1)-category, weak Kan complex, inner Kan complex, ∞-category

In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category. The study of such generalizations is known as higher category theory.

~15 min read

Encyclopedic overview

17 sections
Contents
  • Overview
  • Definition
  • The homotopy category
  • Examples
  • Homotopy coherent nerve
  • Constructions
  • Equivalences between ∞-categories
  • Presheaves
  • Adjunctions
  • Final objects and final maps
  • Presentable ∞-categories
  • Stable ∞-categories
  • Variants
  • See also
  • Notes
  • References
  • External links

In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category. The study of such generalizations is known as higher category theory.

== Overview == Quasi-categories were introduced by . André Joyal has much advanced the study of quasi-categories showing that most of the usual basic category theory and some of the advanced notions and theorems have their analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories has been expounded by .

Excerpted from Wikipedia’s “quasi-category” article, available under the CC BY-SA 4.0 licence.

Available in 7 languages

via Wikidata sitelinks · CC0