Maria Manuel Clementino ; Ignacio Lopez Franco - Lax orthogonal factorisations in monad-quantale-enriched categories

lmcs:2667 - Logical Methods in Computer Science, September 27, 2017, Volume 13, Issue 3 - https://doi.org/10.23638/LMCS-13(3:32)2017
Lax orthogonal factorisations in monad-quantale-enriched categoriesArticle

Authors: Maria Manuel Clementino ORCID; Ignacio Lopez Franco ORCID

We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$ laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of $(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose corresponding weak factorisation system has embeddings as left part. In addition, we present presheaf submonads and study the LOFSs they define. This provides a method of constructing weak factorisation systems on some well-known examples of topological categories over $\mathsf{Set}$.

Comment: 13 pages. Minor changes from previous version

https://doi.org/10.23638/LMCS-13(3:32)2017
Source: arXiv.org:1701.05510
Volume: Volume 13, Issue 3
Secondary volumes: Special Festschrift Issue in Honor of Jiří Adámek
Published on: September 27, 2017
Accepted on: September 1, 2017
Submitted on: September 1, 2017
Keywords: Mathematics - Category Theory
Licence: arXiv.org - Non-exclusive license to distribute
Funding:
    Source : OpenAIRE Graph
  • Center for Mathematics, University of Coimbra; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: UID/MAT/00324/2013

Classifications

Mathematics Subject Classification 20201
Sources:
  • [1] zbMATH Open.

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