Colimits of monoids
Copyright policy )Colimits of monoids
If $\mathcal{C}$ is a cocomplete monoidal category in which tensoring from both sides preserves coequalizers, then the category of monoids over $\mathcal{C}$ is cocomplete. The same holds if $\mathcal{C}$ has regular factorizations and tensoring only preserves regular epimorphisms. As an application a lifting theorem for an adjunction with a monoidal right adjoint to an adjunction between the respective categories of monoids is proved.
10 pages
(regularly) monadic functors, Monoidal, symmetric monoidal and braided categories, Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.), FOS: Mathematics, 18D10, 18A30, monoidal functors, Mathematics - Category Theory, Category Theory (math.CT), monoids in monoidal categories, (reflexive) coequalizers
(regularly) monadic functors, Monoidal, symmetric monoidal and braided categories, Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.), FOS: Mathematics, 18D10, 18A30, monoidal functors, Mathematics - Category Theory, Category Theory (math.CT), monoids in monoidal categories, (reflexive) coequalizers
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