@ARTICLE{Moerdijk02monadson, author = {I. Moerdijk}, title = {Monads on Tensor Categories}, journal = {J. Pure Appl. Algebra}, year = {2002}, volume = {168}, pages = {189--208} }

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Abstract

this paper we will discuss the combination of two classical notions of category theory, both treated extensively in [CWM]. One of these is the notion of a monad or triple on a category, which goes back to Godement [G] and was rst developed by Eilenberg, Moore, Beck and others. The other is that of a monoidal category or tensor category, which originates with Benabou [Be] and with Mac Lane's famous coherence theorem [MacL], and which pervades much of present day mathematics. For a monad S on a tensor category, there is a natural additional structure that one can impose, namely that of a comparison map S(X