Transformation from the List monad to the Bag monad on the 2-Category of Groupoids

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Kock has shown that the Bag monad and the List monad are polynomial on the 2-Category of Groupoids. He even suggests there is a transformation between them (I think, in section 3.10 Examples) going from List to Bag. Can someone present the transformation from List to Bag in gross detail? It seems like I want his short paragraph expanded and given much more detail. It has been pointed out that this transformation is easy to understand, we simply forget the ordering of the lists. Can someone explicitly state how you do this with transformations between monads? It would also be nice to see this reflected in the functor between the category of free commutative monoids and the category of free monoids.




category-theory monads




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  • I don't see the transformation you mention in that section: could you clarify?
    – B. Mehta
    Jul 31 at 16:48










  • "The diagram of groupoids a diagram now represents the cartesian natural transformations, or polymorphic func- tions, from lists to cyclic lists to multisets.
    – Ben Sprott
    Jul 31 at 17:05










  • Upvote this comment if you would like to see a bounty.
    – Ben Sprott
    Aug 2 at 14:39














up vote
1
down vote

favorite












Kock has shown that the Bag monad and the List monad are polynomial on the 2-Category of Groupoids. He even suggests there is a transformation between them (I think, in section 3.10 Examples) going from List to Bag. Can someone present the transformation from List to Bag in gross detail? It seems like I want his short paragraph expanded and given much more detail. It has been pointed out that this transformation is easy to understand, we simply forget the ordering of the lists. Can someone explicitly state how you do this with transformations between monads? It would also be nice to see this reflected in the functor between the category of free commutative monoids and the category of free monoids.




category-theory monads




share|cite|improve this question



















  • I don't see the transformation you mention in that section: could you clarify?
    – B. Mehta
    Jul 31 at 16:48










  • "The diagram of groupoids a diagram now represents the cartesian natural transformations, or polymorphic func- tions, from lists to cyclic lists to multisets.
    – Ben Sprott
    Jul 31 at 17:05










  • Upvote this comment if you would like to see a bounty.
    – Ben Sprott
    Aug 2 at 14:39












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Kock has shown that the Bag monad and the List monad are polynomial on the 2-Category of Groupoids. He even suggests there is a transformation between them (I think, in section 3.10 Examples) going from List to Bag. Can someone present the transformation from List to Bag in gross detail? It seems like I want his short paragraph expanded and given much more detail. It has been pointed out that this transformation is easy to understand, we simply forget the ordering of the lists. Can someone explicitly state how you do this with transformations between monads? It would also be nice to see this reflected in the functor between the category of free commutative monoids and the category of free monoids.




category-theory monads




share|cite|improve this question











Kock has shown that the Bag monad and the List monad are polynomial on the 2-Category of Groupoids. He even suggests there is a transformation between them (I think, in section 3.10 Examples) going from List to Bag. Can someone present the transformation from List to Bag in gross detail? It seems like I want his short paragraph expanded and given much more detail. It has been pointed out that this transformation is easy to understand, we simply forget the ordering of the lists. Can someone explicitly state how you do this with transformations between monads? It would also be nice to see this reflected in the functor between the category of free commutative monoids and the category of free monoids.





category-theory monads





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 31 at 16:33









Ben Sprott

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  • I don't see the transformation you mention in that section: could you clarify?
    – B. Mehta
    Jul 31 at 16:48










  • "The diagram of groupoids a diagram now represents the cartesian natural transformations, or polymorphic func- tions, from lists to cyclic lists to multisets.
    – Ben Sprott
    Jul 31 at 17:05










  • Upvote this comment if you would like to see a bounty.
    – Ben Sprott
    Aug 2 at 14:39
















  • I don't see the transformation you mention in that section: could you clarify?
    – B. Mehta
    Jul 31 at 16:48










  • "The diagram of groupoids a diagram now represents the cartesian natural transformations, or polymorphic func- tions, from lists to cyclic lists to multisets.
    – Ben Sprott
    Jul 31 at 17:05










  • Upvote this comment if you would like to see a bounty.
    – Ben Sprott
    Aug 2 at 14:39















I don't see the transformation you mention in that section: could you clarify?
– B. Mehta
Jul 31 at 16:48




I don't see the transformation you mention in that section: could you clarify?
– B. Mehta
Jul 31 at 16:48












"The diagram of groupoids a diagram now represents the cartesian natural transformations, or polymorphic func- tions, from lists to cyclic lists to multisets.
– Ben Sprott
Jul 31 at 17:05




"The diagram of groupoids a diagram now represents the cartesian natural transformations, or polymorphic func- tions, from lists to cyclic lists to multisets.
– Ben Sprott
Jul 31 at 17:05












Upvote this comment if you would like to see a bounty.
– Ben Sprott
Aug 2 at 14:39




Upvote this comment if you would like to see a bounty.
– Ben Sprott
Aug 2 at 14:39















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