Talk:Monad (category theory)

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[edit] Module (category theory)

Hi there! Does the concept of Module (category theory) make any sense to you? If so, would anybody write an article about this? This article seems to be requested on Wikipedia:Requested articles/mathematics. I suspect the person requesting this article confused something, but I could be wrong. Thanks. Oleg Alexandrov 21:45, 28 Feb 2005 (UTC)

Traditional modules can be thought of as functors by taking a functor from a ring (considered as a category with one element) to abelian groups. One can generalize to modules in other categories and this is mentioned on the module page under generalizations.

[edit] Examples

Can people provide more examples? 137.111.90.68 23:30, 1 November 2007 (UTC)

[edit] Confusing sentence?

"While monads are quite common, making them explicit is less so (the language belongs to the school of Mac Lane, and has rarely been used in the school of Grothendieck, which prefers to write out monads and comonads longhand)." What does it mean, to "write out monads and comonads longhand"? Can anyone clarify? Thanks Sam Staton (talk) 15:19, 23 May 2008 (UTC)

It just means writing down formulae like f_*f^*, for operations on sheaves (usually), rather than saying explicitly that these are adjoint functors and we are taking the (co)monad of the adjunction. Charles Matthews (talk) 07:23, 25 May 2008 (UTC)

Ah, thanks. I've had a go at clarifying that sentence... Sam Staton (talk) 10:23, 25 May 2008 (UTC)