Quasi-category

Summary

A quasi-category is a simplicial set in which every inner horn has a filler. Quasi-categories are the most used model of (∞,1)-categories, developed by Joyal and Lurie. They include both ordinary categories, through their nerves, and Kan complexes, which model $\infty$-groupoids. Much of ordinary category theory, including limits, adjunctions and the Yoneda lemma, extends to quasi-categories.