Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.
I also added a few words in the definition section that seemed to be missing, apologies for the double post.
No problem, I have tidied up the postings :-).
Much appreciated!
added some references:
Francis Borceux, Def. 4.4.1 in: Handbook of Categorical Algebra, Vol. 2: Categories and Structures, Encyclopedia of Mathematics and its Applications 50 Cambridge University Press (1994) [doi:10.1017/CBO9780511525865]
Emily Riehl, §5.3 in: Category Theory in Context, Dover Publications (2017) [pdf]
I have hyperlinked all occurrences of “comparison functor” on this page, and am giving this is own page now.
added the proposition (here) that monadic functors create limits
(copied over from the created limit)
1 to 13 of 13