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Eduardo Ochs (Jul 30 2020 at 02:52):People, what are your favorite references on Kan extensions? I'm trying to understand the proof that the formula for Kan extensions, , works, but I am having a hard time on it... I am trying to read the proof in both in CWM and in Emily Riehl's "Categories in Context"...
Eduardo Ochs (Jul 30 2020 at 02:55):My notes are here, but ATM the material on Kan extensions in them stops right after I show how to visualize what the formula above "means" (in section 7.11).
http://angg.twu.net/LATEX/2020favorite-conventions.pdf
Thomas Read (Jul 30 2020 at 12:03):You might be interested in the co/end approach to this - in particular you can write the limit formula you gave as an end, and there's a very short (although not necessarily enlightening) proof that this formula is correct using co/end calculus. See e.g. Proposition 2.3.5 in Fosco Loregian's book (https://arxiv.org/pdf/1501.02503.pdf)
Eduardo Ochs (Jul 30 2020 at 17:49):Thomas Read said:
You might be interested in the co/end approach to this - in particular you can write the limit formula you gave as an end, and there's a very short (although not necessarily enlightening) proof that this formula is correct using co/end calculus. See e.g. Proposition 2.3.5 in Fosco Loregian's book (https://arxiv.org/pdf/1501.02503.pdf)
Thanks!!! It look very nice but it has lots of prerequisites - I'll try to decypher in it parallel with the proofs in Riehl and in CWM! =)