Original Articles

On Categories of Monoids, Comonoids, and Bimonoids


Abstract

The categories of monoids, comonoids and bimonoids over a symmetric monoidal category C are investigated. It is shown that all of them are locally presentable provided C's underlying category is. As a consequence numerous functors on and between these categories are shown to be part of an adjoint situation; in particular, the category of comonoids is monoidally closed.

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