Simplicial sets

Simplicial sets are mathematical structures that generalize shapes and spaces by assembling basic building blocks called simplices—points, line segments, triangles, and their higher-dimensional counterparts. They organize how these pieces are connected and related, allowing mathematicians to study complex geometric forms and topological properties in a combinatorial way. Think of them as a flexible blueprint for breaking down and reconstructing shapes, making it easier to analyze their structure and features in fields like algebraic topology and geometry.