Simplicial set

A simplicial set is a mathematical structure that formalizes the idea of building complex shapes from simple building blocks called simplices—points, line segments, triangles, and higher-dimensional analogues. It encodes how these pieces fit together, allowing mathematicians to study the shape's structure and properties in a flexible, algebraic way. Think of it as a combinatorial blueprint of a geometric object, capturing both its parts and the way they connect, enabling analysis of shapes that can be very high-dimensional or abstract.