# Nerve (category theory)

## Simplicial set constructed from the objects and morphisms of a small category / From Wikipedia, the free encyclopedia

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In category theory, a discipline within mathematics, the **nerve** *N*(*C*) of a small category *C* is a simplicial set constructed from the objects and morphisms of *C*. The geometric realization of this simplicial set is a topological space, called the **classifying space of the category** *C*. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory.

Simplicial set constructed from the objects and morphisms of a small category

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