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7
votes
Accepted
What is the (Co)Monad for a Bag
The answer is essentially already in the comments. Commutativity erases a monoid's sense of order, so the free commutative monoid monad is the 'bag monad' even if the free monoid monad is the 'list mo …
6
votes
What categories correspond to the typed lambda calculus with parametric types?
The internal language of a locally Cartesian closed category is a dependent type theory. A category $\mathcal C$ is locally Cartesian closed, if all of its slices $\mathcal C/X$ are Cartesian closed. …