A simplicial set is a fundamental concept in algebraic topology and category theory that generalizes the notion of a topological space. It is a combinatorial structure used to study objects in homotopy theory and other areas of mathematics. ### Definition A **simplicial set** consists of: 1. **Sets of n-simplices**: For each non-negative integer \( n \), there is a set \( S_n \) which consists of n-simplices.
Articles by others on the same topic
A simplicial set is a functor from the opposite of the simplex category to sets. Its face and degeneracy maps satisfy the simplicial identities.