The theory of quasi-categories

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**Higher category theory**
##Contents
* Contributors
* References
* Introduction
* The theory of quasi-categories
* The theory of n-quasi-categories
***
**Categorical mathematics**
##Contents
* Set theory
* Category theory
* Homotopical algebra
* Higher category theory
* Theory of quasi-categories
* Higher quasi-categories
* Geometry
* Elementary geometry
* Differential geometry
* Lie theory
* Algebraic geometry
* Homotopical algebraic geometry
* Number theory
* Elementary number theory
* Algebraic number theory
* Algebra
* Universal algebra
* Group theory
* Rings and modules
* Commutative algebras
* Lie algebras
* Representation theory
* Operads
* Homological algebra
* Logic
* Boolean algebra
* First order theory
* Model theory
* Categorical logic
* Topology
* General topology
* Algebraic topology
* Homotopy theory
* Theory of locales
* Topos theory
* Higher topos theory
* Combinatorics
* Combinatorial geometry
* Enumerative combinatorics
* Algebraic combinatorics

The notion of quasi-category was introduced by Michael Boardman and Rainer Vogt in their book *Homotopy Invariant Algebraic Structures in Topological Spaces*. A Kan complex and the nerve of a category are basic example. A quasi-category is sometime called a *weak Kan complex* in the literature. We have introduced the term *quasi-category* in order to stress the similarity between category theory and the theory of quasi-categories. We shall often use the term *quategory* as an abreviation for quasi-category.

It turns out that essentially all of category theory can be extended to quasi-categories. The resulting theory has applications to homotopy theory, homotopical algebra, higher category theory and higher topos theory.

- Michael Boardman,Rainer Vogt,
*Homotopy invariant algebraic structures in Topological Spaces*, Springer Lecture Notes in Math, 347.

Revised on May 10, 2013 at 09:45:35
by
Tim Porter