2014/09/11 by Jiřı́ Adámek, Jiří Adámek, Adámek, Jiří
Computer Science · Mathematics · #FOS: Computer and information sciences #History and Theory of Mathematics #Logic in Computer Science (cs.LO) #Mathematics and Applications #cs.LO
paper · pdf · doi:10.48550/arxiv.1409.3805
arxiv created 2014/09/11 · openalex publication_date 2014/09/11 · arxiv updated 2014/09/15 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The category of all monads over many-sorted sets (and over other "set-like" categories) is proved to have coequalizers and strong cointersections. And a general diagram has a colimit whenever all the monads involved preserve monomorphisms and have arbitrarily large joint pre-fixpoints. In contrast, coequalizers fail to exist e.g. for monads over the (presheaf) category of graphs. For more general categories we extend the results on coproducts of monads from [2]. We call a monad separated if, when restricted to monomorphisms, its unit has a complement. We prove that every collection of separated monads with arbitrarily large joint pre-fixpoints has a coproduct. And a concrete formula for these coproducts is presented.