I have questions about the kleisli category of the continuation monad K_R on the category of sets
1. I think that the kleisli category is independent of the choice of R (up to equivalence) as long as R has cardinality at least 2, so there are many monads but they all share the same kleisli category. Is that correct?
2. The kleisli categories have coproducts (as all kleisli categories do) and it is coclosed. The cartesian product of sets fails to lift to a monoidal product, it's only premonoidal. Does the kleisli category have any monoidal structures other than the coproduct?
julesh
npub162…vlr5t
2025-10-11 12:45:42 UTC
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2025-10-11 12:45:42 UTCEvent JSON
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"content": "I have questions about the kleisli category of the continuation monad K_R on the category of sets\n\n1. I think that the kleisli category is independent of the choice of R (up to equivalence) as long as R has cardinality at least 2, so there are many monads but they all share the same kleisli category. Is that correct?\n\n2. The kleisli categories have coproducts (as all kleisli categories do) and it is coclosed. The cartesian product of sets fails to lift to a monoidal product, it's only premonoidal. Does the kleisli category have any monoidal structures other than the coproduct?",
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