The theory of quasi-categories

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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