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I began adding proofs of Lemma 1-4 to the page transfinite construction of free algebras. The layout of the two array environment has to be fixed; proof of 3-4 to be added.
Any help/suggestion is extremely appreciated!
Well, Theorem 2 is about algebras for a pointed endofunctor rather than for a monad. In the monad case, you’d need to -reduce the proof of Theorem 3.
Dmitri: I don’t know the answer but I’m interested.
I began interesting myself in the topic because of this question:
Take a (well-)pointed endofunctor and consider for any object the -chain
its colimit should define a new pointed (because of the UMP of colimit) , which I expect to have some “nice” property. Initially I thought it was sort of the free monad attached to ; but a rapid computation gives a transformation in the wrong direction, .
Maybe one is able to obtain ? If yes, in which way? Before adding this new question I decided to go deeper in the study of Kelly’s “And so on” paper, and here am I! :)
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