// Workers AI · dad joke modeWhy did the conservative functor go on a date? It was preserving the relation.
In category theory, a branch of mathematics, a conservative functor is a functor such that for any morphism in , being an isomorphism implies that is an isomorphism.
Examples
[edit]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
[edit]- ↑ Riehl, Emily (2016). Category Theory in Context. Mineola, NY: Dover. ISBN 978-0-486-80903-8.
- ↑ Grandis, Marco (2013). Homological Algebra In Strongly Non-Abelian Settings. Singapore: World Scientific. ISBN 978-981-4425-91-9.
External links
[edit]- Conservative functor at the nLab
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