On the Category of Partial Bijections

TL;DR

This paper characterizes the category of partial bijections as an inverse-Baer*-category with specific properties and establishes Noether isomorphism theorems within this framework, advancing the theoretical understanding of such categories.

Contribution

It proves that the category of partial bijections is an inverse-Baer*-category with closed projections and an exact idempotent split, and formulates Noether isomorphism theorems for it.

Findings

Category of partial bijections is an inverse-Baer*-category

It has closed projections and is an exact category

Noether isomorphism theorems are established for this category

Abstract

Categories of partial functions have become increasingly important principally because of their applications in theoretical computer science. In this note we prove that the category of partial bijections between sets as an inverse-Baer*-category with closed projections and in which the idempotent split is an exact category. Finally the Noether isomorphism theorems are given for this exact category.