This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from

Simplicial sets are discrete analogs of topological spaces. They have played a central role in algebraic topology ever since their introduction in the late 1940

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.

The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many othe

Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic the