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
Page Template:Reflist/styles.css has no content.
- ^ Page Module:Citation/CS1/styles.css has no content.Riehl, Emily (2016). Category Theory in Context. Courier Dover Publications. ISBN 048680903X. Retrieved 18 February 2017.
- ^ Page Module:Citation/CS1/styles.css has no content.Grandis, Marco (2013). Homological Algebra: In Strongly Non-Abelian Settings. World Scientific. ISBN 9814425931. Retrieved 14 January 2017.
External links
- REDIRECT Template:Category theory
- From a merge: This is a redirect from a page that was merged into another page. This redirect was kept in order to preserve the edit history of this page after its content was merged into the content of the target page. Please do not remove the tag that generates this text (unless the need to recreate content on this page has been demonstrated) or delete this page.
- For redirects with substantive page histories that did not result from page merges use Template:Tl instead.
