Dilatations of categories
Arnaud Mayeux
TL;DR
This paper introduces the concept of dilatations in categories, a formal construction that generalizes localizations and ring dilatations, and studies their properties and examples.
Contribution
It formalizes dilatations of categories via a universal property, expanding the understanding of category modifications beyond existing concepts.
Findings
Dilatations generalize localizations of categories.
Dilatations of rings are examples of this construction.
The paper provides foundational properties and examples of dilatations.
Abstract
Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories include localizations of categories and dilatations of rings.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra