Normalizers and split extensions
Dominique Bourn, James Richard Andrew Gray
TL;DR
This paper explores the structural role of normalizers in category theory, linking their existence to cartesian maps associated with the kernel functor, revealing a broader underlying phenomenon.
Contribution
It explicitly characterizes the structural phenomenon behind normalizers using cartesian maps and kernel functors, providing new insights into their theoretical foundations.
Findings
Normalizers are linked to cartesian maps related to kernel functors.
A broader structural phenomenon behind normalizers is identified.
The work clarifies the categorical role of normalizers in a new framework.
Abstract
We make explicit a larger structural phenomenon hidden behind the existence of normalizers in terms of existence of certain cartesian maps related to the kernel functor.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic Geometry and Number Theory