Isomorphism theorems and descent in star-regular categories
(2014)
Files
NgahaThesis.pdf
Open Access - Adobe PDF
- 964.4 KB
Details
- Authors
- Supervisors
- Gran, Marino
- Abstract
- The concept of star-relation has been shown to be suitable to unify and compare many results in pointed and non-pointed categorical algebra. In particular, the notion of star-regular category can be seen as a common generalization of the classical notion of regular category (in the total context) and of normal category (in the pointed context). Many categories investigated in universal algebra (groups, rings, Lie algebras, modules over a commutative ring) and in functional analysis (Banach spaces, locally compact abelian groups, topological groups) are star-regular categories. The main goal of this thesis is to study two fundamental aspects of star-regular categories. We first show that a general version of the Noether isomorphism theorems and of the Zassenhaus Lemma hold in these categories. We then introduce the notion of semi-effective star-regular category in order to investigate descent theory. In particular we prove that regular epimorphisms are effective descent morphisms in these categories. This result applies to any ideal determined category, to any almost abelian category, and to any efficiently regular category.
- Affiliations
Citations
Ngaha Ngaha, M. O. (2014). Isomorphism theorems and descent in star-regular categories. https://hdl.handle.net/2078.5/48936