# Joyal's CatLab The theory of quasi-categories

Higher category theory

***

Categorical mathematics

# Idea

###### Origin

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.

# References

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