Examples
Examples of regular categories include:
- Set, the category of sets and functions between the sets
- More generally, every elementary topos
- Grp, the category of groups and group homomorphisms
- The category of fields and ring homomorphisms
- Every bounded join-semilattice, with morphisms given by the order relation
- Abelian categories
The following categories are not regular:
- Top, the category of topological spaces and continuous functions
- Cat, the category of small categories and functors
Read more about this topic: Regular Category
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