Conservative functor

From Wikipedia, the free encyclopedia

In category theory, a branch of mathematics, a conservative functor is a functor such that for any morphism f in C, F(f) being an isomorphism implies that f is an isomorphism.

Examples

The forgetful functors in algebra, such as from Grp to Set, are conservative. More generally, every monadic functor is conservative.[1] In contrast, the forgetful functor from Top to Set is not conservative because not every continuous bijection is a homeomorphism.

Every faithful functor from a balanced category is conservative.[2]

References

Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.