Timeline for Partially fibered categories vs T-Multicategories
Current License: CC BY-SA 4.0
6 events
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| Sep 30, 2019 at 15:02 | comment | added | Simon Henry | @TimCampion : Yes absolutely, this definition in term of partial fibration has the advantages of being very easy to generalize to higher categories. And this is indeed the sort of thing that is behind Lurie's definition of operad (that's bascially what I'm refering too in the last paragraph) | |
| Sep 30, 2019 at 14:46 | comment | added | Tim Campion | 3) I think this perspective is also closely related to Lurie's operad formalism, where an operad is a certain kind of category over $Fin_\ast$ -- you can think of $Fin_\ast$ as sitting inside $FinSpan$, and then I think you can rework the whole thing as a category over $FinSpan$ with certain cocartesian lifts and certain representability conditions. $FinSpan$ can be thought of as the Kleisli category of the free-symmetric-monoidal-category monad, restricted to finite sets. | |
| Sep 30, 2019 at 14:43 | comment | added | Tim Campion | Here are a few more comments that won't actually answer the question :). 1) If you're interested in generalizing to non-cartesian monads, then you should look at Cruttwell and Shulman if you haven't already. 2) Your discussion reminds me of Street's description of the Eilenberg-Moore category as a category of presheaves on the Kleisli category satisfying representability conditions. Perhaps there's a description of T-multicategories where the representability is relaxed... | |
| Sep 30, 2019 at 14:23 | comment | added | Simon Henry | @TimCampion : Thanks for the reference, I didn't know these papers. They do not seem to contain the result I'm after though. | |
| Sep 29, 2019 at 19:15 | comment | added | Tim Campion | I think the work of Hermida should be relevant. I'm not quite sure which paper is most so, but you might start with this one. Or maybe this one. | |
| Sep 29, 2019 at 14:31 | history | asked | Simon Henry | CC BY-SA 4.0 |