Lax orthogonal factorisations in monad-quantale-enriched categories
We show that, for a quantale V and a Set-monad T laxly extended to V-Rel, the presheaf monad on the category of (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 p...
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| Format: | article |
| Language: | eng |
| Published: |
2017
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| Online Access: | http://hdl.handle.net/10316/89419 |
| Country: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/89419 |
| Summary: | We show that, for a quantale V and a Set-monad T laxly extended to V-Rel, the presheaf monad on the category of (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 Set. |
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