quasi-category
Sign in to saveAlso 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 sectionsContents
- 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.