[[Skeletal category]]
# Skeleton category

Let $\cat C$ be a [[category]].
A **skeleton** $\opn{Sk} \cat C$ is a [[Skeletal category|skeletal]] [[subcategory]] whose inclusion functor makes it [[Equivalence of categories|equivalent]] to $\cat C$. #m/def/cat 
Thus, an object in $\opn{Sk} \cat C$ is a representative of an [[isomorphism class]] in $\cat C$.
While this construction is not generally unique, 
the precise selection of representatives usually doesn't matter.

## Properies

- [[Categories are equivalent iff they have isomorphic skeleta]]

## Examples

- [[Category of natural numbers]] is a skeleton of [[Category of finite sets]]

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#state/tidy | #lang/en | #SemBr