Pretorsion theories in lextensive categories
Francis Borceux, Federico Campanini, Marino Gran
TL;DR
This paper introduces a construction for stable categories within pretorsion theories in lextensive categories, extending previous results and providing examples in topology and category theory.
Contribution
It develops a universal construction for stable categories in pretorsion theories in lextensive categories, generalizing prior work on internal preorders.
Findings
Established a universal property for the stable category construction.
Extended previous results from pretopos to lextensive categories.
Provided concrete examples in topology and small categories.
Abstract
We propose a construction of a stable category for any pretorsion theory in a lextensive category. We prove the universal property of the stable category, that extends previous results obtained for the stable category of internal preorders in a pretopos. Some examples are provided in the categories of topological spaces and of (small) categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Fuzzy and Soft Set Theory