Monomorphisms, Epimorphisms, and Pull-Backs

On Strong Monomorphisms and Strong Epimorphisms

M. A. Al Shumrani Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Correspondence should be addressed to M. A. Al Shumrani, [email protected] Received 10 March 2010; Accepted 5 May 2010 Academic Editor: Mihai Putinar Copyright q 2010 M. A. Al Shumrani. This is an open access article distributed under the Creative Commons Attribution License,...

On Epimorphisms and Monomorphisms of Hopf Algebras

We notice that for a Hopf algebra H , its antipode S is both an epimorphism and a monomorphism from H to H in the category of Hopf algebras over a field. Together with the existence of Hopf algebras with non-injective or non-surjective antipode, this proves the existence of non-surjective epimorphisms and non-injective monomorphisms in the category of Hopf algebras. Using Schauenburg’s free Hop...

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

Pull-backs of Bundles and Homotopy Invariance

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over paracompact manifolds, there is a principal fibre bundle isomorphism between pull-backs obtained from homoto...

Reflexive Pull-backs and Base Extension

We prove that Viehweg’s moduli functor of stable surfaces is locally