Locally small category

Revision as of 15:13, 19 November 2009 by Boy Soprano II (talk | contribs) (definition; an example)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

A locally small category is a category whose hom-sets are (small) sets. More explicitly, it is a category such that for all objects $A$ and $B$ in the category, there exists a set $\text{Hom}(A,B)$ whose elements are exactly the morphisms from $A$ to $B$.

Most categories encountered outside category theory are locally small. For example, the category of sets is a locally small category, even though it is not a small category. This is because there is no (small) set containing all (small) sets, but for any two sets $A$ and $B$, there does exist a set $\text{Hom}(A,B)$ that contains all the morphisms from $A$ to $B$, i.e., all the functions $f : A \to B$.

This article is a stub. Help us out by expanding it.

See also