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Joachim Kock (Mar 14 2022 at 13:37):The 2022 Workshop on Polynomial Functors is starting now!
Here is the website:
https://topos.site/p-func-workshop/
Joachim Kock (Mar 14 2022 at 13:39):Here is the list of speakers:
● Steve Awodey x2: Tutorial: Polynomial functors and type theory
● Kristine Bauer: Categorical differentiation and Goodwillie polynomial functors
● Clemens Berger: Goodwillie's cubical cross-effects and nilpotency in semiabelian categories
● Pierre-Louis Curien: Opetopes, opetopic sets and polygraphs
● Elden Elmanto: Bispans in algebraic geometry
● Eric Finster: Polynomial Monads and Opetopic Types in Type Theory
● Marcelo Fiore: Polynomial modelling of abstract syntax
● Nicola Gambino: The matrix product of coloured symmetric sequences
● Brenda Johnson: From polynomial functors to functor calculi
● Sean Moss: Dependent products of polynomials
● Fredrik Nordvall Forsberg: On the differential structure of polynomial functors
● Exequiel Rivas: Procontainers: a proposal from computational effects
● Brandon Shapiro: Familial Monads for Higher and Lower Category Theory
● David Spivak: Functorial aggregation
● Paul Taylor: The Berry Order (Ideas from 1980s stable domain theory)
● Todd Trimble: Notions of functor for Poly
● Christine Vespa x3: Tutorial: Eilenberg-Mac Lane polynomial functors
Joshua Meyers (Mar 17 2022 at 01:48):Hi all, it looks like tomorrow there will be two talks about the Eilenberg-MacLane notion of polynomial functors, which Christine Vespa has talked about the past three days. While I enjoyed Christine's talks, I still don't see the motivation for this notion, perhaps because of lack of background in the algebraic topology that motivated Eilenberg and MacLane. Is it possible to motivate this notion, given that I already care about the modern notion of polynomial functors, as in the work of David Spivak?
Tim Hosgood (Mar 17 2022 at 01:59):as in, you're happy with hearing some algebraic topology motivation because you're not familiar with it, or you'd like to hear some motivation purely in terms of polynomial functors in the other sense?
Tim Hosgood (Mar 17 2022 at 01:59):I think a few people can give you the former, but from what I gather, one of the purposes of this conference is to come up with a good answer to the latter!
Joshua Meyers (Mar 17 2022 at 06:43):The latter! I'm afraid I wouldn't know enough algebraic topology to understand the former
Nathanael Arkor (Mar 17 2022 at 13:47):I think a few people can give you the former, but from what I gather, one of the purposes of this conference is to come up with a good answer to the latter!
Do you know if there's any indication there is a connection? It feels a little like this is the conjunction of two conferences, but I think I missed the justification (if it was mentioned at some point).
Nathanael Arkor (Mar 17 2022 at 13:48):That is, there are many things in mathematics with the same name, yet are unrelated.
Nathanael Arkor (Mar 17 2022 at 13:48):Is there an indication this is not true for the two meanings of "polynomial functor"?
Tim Hosgood (Mar 17 2022 at 13:49):well they are both functors that are really very much actually polynomials, so it feels weird that they might not be related, but... i don't know :shrug:
Tim Hosgood (Mar 18 2022 at 14:34):so it looks like the current talk might answer exactly this question!
Tim Hosgood (Mar 18 2022 at 14:35):polynomial functors are sent to polynomial functors via a spectrum functor!
Tim Hosgood (Mar 18 2022 at 14:40):that is, from what i understand, the "polynomial-ness" of the functors in both senses actually do agree, and there's a very nice functor which witnesses this and shows how LCC polynomial turns into EM polynomial