Category Theory
Zulip Server
Archive

You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.

Stream: deprecated: mathematics

Topic: Internal Categories in Poly and monad structure

Ben Sprott (Dec 08 2020 at 01:58):

Here we see Spivak defining Categories as comonoids in the monoidal category $(Poly, \circ, y)$, section 2.5. Comonoids in an endofunctor category are comonads. I would guess that if you add a monad structure to your comonoids, you still have a category, but you have extra structure. It would be interesting to know what extra stuff you are endowing the category with if you add monad structure.