A constructive approach to the double-categorical small object argument

Fuente: arXiv
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Autori principali: Berg, Benno van den, Bourke, John, Seip, Paul
Natura: Preprint
Pubblicazione: 2025
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author Berg, Benno van den
Bourke, John
Seip, Paul
author_facet Berg, Benno van den
Bourke, John
Seip, Paul
contents Bourke and Garner described how to cofibrantly generate algebraic weak factorisation systems by a small double category of morphisms. However they did not give an explicit construction of the resulting factorisations as in the classical small object argument. In this paper we give such an explicit construction, as the colimit of a chain, which makes the result applicable in constructive settings; in particular, our methods provide a constructive proof that the effective Kan fibrations introduced by Van den Berg and Faber appear as the right class of an algebraic weak factorisation system.
format Preprint
id arxiv_https___arxiv_org_abs_2512_11692
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A constructive approach to the double-categorical small object argument
Berg, Benno van den
Bourke, John
Seip, Paul
Category Theory
Logic
Bourke and Garner described how to cofibrantly generate algebraic weak factorisation systems by a small double category of morphisms. However they did not give an explicit construction of the resulting factorisations as in the classical small object argument. In this paper we give such an explicit construction, as the colimit of a chain, which makes the result applicable in constructive settings; in particular, our methods provide a constructive proof that the effective Kan fibrations introduced by Van den Berg and Faber appear as the right class of an algebraic weak factorisation system.
title A constructive approach to the double-categorical small object argument
topic Category Theory
Logic
url https://arxiv.org/abs/2512.11692