Skeletal category

Skeleton category

Let 𝖢 be a category. A skeleton Sk⁡𝖢 is a skeletal subcategory whose inclusion functor makes it equivalent to 𝖢. cat Thus, an object in Sk⁡𝖢 is a representative of an isomorphism class in 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

---

tidy | en | SemBr