On semiabelian categories in Functional Analysis and Topological Algebra

TL;DR

This paper provides an elementary, self-contained overview of semiabelian categories, illustrating their fundamental examples in Functional Analysis and Topological Algebra, highlighting their significance beyond abelian categories.

Contribution

It offers a clear presentation of semiabelian categories and details key examples in Functional Analysis and Topological Algebra, expanding understanding of non-abelian categorical structures.

Findings

Detailed examples of semiabelian categories in Functional Analysis

Illustration of semiabelian categories in Topological Algebra

Clarification of the non-abelian structure in these contexts

Abstract

In this work we discuss an elementary self-contained presentation of the notion of a semiabelian category, introduced by Raikov and Palamodov. Fundamental examples of (non-abelian) semiabelian categories occuring in Functional Analysis and Topological Algebra are treated in detail throughout the paper.