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
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)