Hi Co, (This email in a gist in case the ASCII art below gets lost in translation https://gist.github.com/Lysxia/d81abf4e35e8094df0a92ec5ff1467da) Categorically, we prefer looking at a monoid (Z, 1, (*)) as a pair of morphisms (functions in Set) (const 1 : () -> Z) and (uncurry (*) : Z x Z -> Z). A monoid homomorphism is_odd : Z -> B is a morphism which makes the following diagrams commute: const 1 () ------------> Z | | id | | is_odd | | v v () ------------> B const True (*) Z x Z ---------> Z | | is_odd *** is_odd | | is_odd | | v v B x B ---------> B (&&) Cheers, Li-yao On 2022-09-22 10:03 AM, coplot coplot wrote: Hello every one, I'm reading "Programming with Categories Brendan Fong Bartosz Milewski David I. Spivak" and here there's an example of monoid in Haskell: /Consider the monoidsZ×�(Z,1,×)andBAND�(B,true,AND).Let is_odd:Z→Bbe the function that sends odd numbers totrueand even numbers to false. This is a monoid homomorphism. It preserves identities because1is odd, and it preserves composition because the product of any two odd numbers is odd, but the product of anything with an even number is even./ I'd like representing it graphically I mean the object Zx and arrows about is_odd function, but I do not know how can do it. This is a valid example of monoid homomorphism and I'd like to know the Haskell implementation and the corresponding categorically view. Thanks Co _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.