The defect functor of a homomorphism and direct unions

Simion Breaz; Jan Žemlička

The defect functor of a homomorphism and direct unions

Representation Theory 2014-10-13 v2 Category Theory Rings and Algebras

Authors: Simion Breaz , Jan Žemlička

Abstract

We will study commuting properties of the defect functor $\mathrm{Dev}_\beta=\mathrm{Coker}\mathrm{Hom}_\mathcal{C}(\beta,-)$ associate to a homomorphism $\beta$ in a finitely presented category. As an application, we characterize objects $M$ such that $\mathrm{Ext}^1_\mathcal{C}(M,-)$ commutes with direct unions (i.e. direct limits of monomorphisms), assuming that $\mathcal{C}$ has a generator which is a direct sum of finitely presented projective objects.

Keywords

defect functor homomorphism direct unions finitely presented category Ext functor direct limits

Cite

@article{arxiv.1408.2016,
  title  = {The defect functor of a homomorphism and direct unions},
  author = {Simion Breaz and Jan Žemlička},
  journal= {arXiv preprint arXiv:1408.2016},
  year   = {2014}
}

Comments

27 pages; v2: references have been updated and completed, and some proofs have been shortened

The defect functor of a homomorphism and direct unions

Abstract

Keywords

Cite

Comments

Related papers