Monads on Symmetric Monoidal Closed Categories By
نویسنده
چکیده
Introduction. This note is concerned with "categories with internal horn and | and we shall use the terminology from the paper [2] by EIL~.NBERG and Kv.Imy. The result proved may be stated briefly as follows : a Y/--monad ("strong monad") on a symmetric monoidal closed category ~ carries two canonical structures as closed functor. I f these agree (in which case we call the monad commutative), tha t structure makes the monad into a closed monad, i.e. a monad in the hypercategory of closed categories. In a subsequent note [3] we are going to show how a commutat ive monad on a symmetric monoidal closed category has for its category of algebras a category which is itself closed in a canonical way (thus extending a theorem of LnCTO~I [4]).
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