Talk:Monad (category theory)

message: Can people provide more examples? 137.111.90.68 23:30, 1 November 2007 (UTC)
thread_title: [[Examples]]

message: In the introduction to this article it is said that a Kleisli triple is also an endofunctor together with two natural transformations just like a monad. But this is factually wrong although we can construct a Kleisli triple from a monad and vice versa. A Kleisli triple is a map of objects (not a functor which would also comprise a map of morphisms) together with a map between hom sets and a natural transformation. From my point of view it would make sense to either have a section devoted to Kleisli triples and their relationship with monads or remove the mention of a Kleisli triple completely.  — Preceding unsigned comment added by 134.106.29.176 (talk) 14:57, 31 October 2012 (UTC)
replies: text: Looks like its fixed to me, and Kleisli triple now covers the topic. 99.153.64.179 (talk) 19:10, 25 June 2013 (UTC)
thread_title:  Monad and Kleisli triple are different structures 

message: Are we sure that MacLane intended the term in its philosophical sense? I'd always heard that it was simply a portmanteau of monoid and triad (as triad and triple were common terms for this concept early on, and the connection to monoids is obvious).
Cgibbard (talk) 04:41, 23 March 2014 (UTC)
replies: text: I agree with Cgibbard. The quote referenced in the article explains nothing about Mac Lane's etymological intention.  Suppose the concept of monad in category theory has any implications for monad in philosophy, it has nothing to do with its etymology by itself. In terms of etymology, a comment in this page is a good summary, and at least, there seems to be no reason to credit monad in category theory to monad in philosophy. There should be some concrete source to refer to monad in philosophy in the article. --Nolze (talk) 13:50, 13 December 2014 (UTC)
thread_title:  Etymology? 

message: Kleisli category is a separate article, whereas Eilenberg-Moore category redirects to Monad. I'd like to add an article for E-M too, but I'd like some feedback first on whether it's warranted. askyle (talk) 15:50, 20 May 2014 (UTC)
thread_title:  Does Eilenberg-Moore category deserve its own article? 

message: "The importance of the definition comes in a class of theorems from the categorical (and algebraic geometry) theory of descent. What was realised in the period 1960 to 1970 is that recognising the categories of coalgebras for a comonad was an important tool of category theory (particularly topos theory). The results involved are based on Beck's theorem. Roughly what goes on is this: while it is simple set theory that a surjective mapping of sets is as good as the equivalence relation "x is in the same fiber as y" on the domain of the mapping, for geometric morphisms what you should do is pass to such a coalgebra subcategory."
This might sound nice to an expert, but it actually makes no sense to someone who is not already on a high level in category AND topos theory. I would recommend to rewrite or cancel it. Saves this gibberisch for the nLab.  — Preceding unsigned comment added by 37.120.66.60 (talk) 16:48, 3 November 2015 (UTC)
thread_title:  Unclear subsection 

message: Hi everyone,
Does anybody know of a reference which discusses coalgebras over (co)monads? I'm wondering how hopf-algebras integrate into this framework. Wundzer (talk) 16:43, 21 January 2021 (UTC)
thread_title:  Co-algebras and comonads