## Clementino, Maria Manuel and Franco, Ignacio Lopez - Lax orthogonal factorisations in monad-quantale-enriched categories

lmcs:2667 - Logical Methods in Computer Science, September 27, 2017, Volume 13, Issue 3
Lax orthogonal factorisations in monad-quantale-enriched categories

Authors: Clementino, Maria Manuel and Franco, Ignacio Lopez

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 $\mathsf{Set}$.

Source : oai:arXiv.org:1701.05510
DOI : 10.23638/LMCS-13(3:32)2017
Volume: Volume 13, Issue 3
Published on: September 27, 2017
Submitted on: September 1, 2017
Keywords: Mathematics - Category Theory

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