Geodesic
Colimits of monoids
Theory and applications of categories, Tome 34 (2019), pp. 456-467.

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If C is a monoidal category with reflexive coequalizers which are preserved by tensoring from both sides, then the category MonC of monoids over C has all coequalizers and these are regular epimorphisms in C. This implies that MonC has all colimits which exist in C, provided that C in addition has (regular epi, jointly monomorphic)-factorizations of discrete cones and admits arbitrary free monoids. A further application is a lifting theorem for adjunctions with a monoidal right adjoint whose left adjoint is not necessarily strong to adjunctions between the respective categories of monoids.
Publié le :
Classification : Primary 18D10, Secondary 18A30
Keywords: Monoids in monoidal categories, (reflexive) coequalizers, (regularly) monadic functors, monoidal functors 
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     author = {Hans-E. Porst},
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Hans-E. Porst. Colimits  of monoids. Theory and applications of categories, Tome 34 (2019), pp. 456-467. http://geodesic.mathdoc.fr/item/TAC_2019_34_a16/