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]

gollark: Bad OS dev, I'm sure.
gollark: You can't actually capture output, only return values.
gollark: Bullies MAY be subject to orbital laser strikes which we definitely have.
gollark: I wonder if the music player in my cube is turned on.
gollark: SOME would say that.

References
  1. Riehl, Emily (2016). Category Theory in Context. Courier Dover Publications. ISBN 048680903X. Retrieved 18 February 2017.
  2. Grandis, Marco (2013). Homological Algebra: In Strongly Non-Abelian Settings. World Scientific. ISBN 9814425931. Retrieved 14 January 2017.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.