Conservative functor
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
External links
- Conservative functor at the nLab
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Functor types
- Additive
- Adjoint
- Conservative
- Derived
- Diagonal
- Enriched
- Essentially surjective
- Exact
- Forgetful
- Full and faithful
- Logical
- Monoidal
- Representable
- Smooth
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