No, I mean monads :) I've never thought of them as of monoids in the endofunctor category. 2009/1/21 David Leimbach :

You mean monoids right? :-)

On Wed, Jan 21, 2009 at 1:30 AM, Eugene Kirpichov wrote:

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Wow. This is a cool point of view on monads, thank you for enlightening (the arrow stuff is yet too difficult for me to understand)!

2009/1/21 Andrzej Jaworski :

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Monads are monoids in categories of functors C -> C Arrows are monoids in subcategories of bifunctors (C^op) x C -> C Trees are a playing ground for functors in general:-)

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Category Theory should speak for itself and I am so glad you guys have seen the beauty of this approach. Yes, Mauro you are right: locally small Freyd categories correspond to monoidal structure of Arrows, but the strength in this correspondence is as yet unknown to me. I disagree however with your doubts: Arrows indeed are Monoids! [in the functor category (C^op) x C -> C with st, cost, ist.] I will skip Monoid ubiquity in linguistics and its relevance to concurrency as not helpful in learning Haskell. (e.g. http://www.springerlink.com/content/7281243255312730/?p=4dd8bba881cd4ebe894d3b014f01b1ad&pi=7) Instead I will issue a guarantee that the time invested in CT will pay also in system analysis, particularly in combination with Haskell type classes, which together might be used for describing real world processes and knowledge. Few have scratched the subject as yet but the pay-off is huge. Let me also suggest to bestow the official guru status on Dan Piponi and Heinrich Apfelmus:-) Cheers, -Andrzej