5
$\begingroup$

A premanifold is a locally ringed space locally isomorphic to an open subset of Euclidean space equipped with its sheaf of smooth functions. No assumption of paracompactness or the Hausdorff property.

What are the regular monomorphisms in this category? What are the regular epimorphisms? What are the universally regular epimorphisms - are they precisely the surjective submersions?

Does anything change for manifolds?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.