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Stream: theory: category theory

Topic: A neat paper

Brendan Murphy (May 10 2024 at 01:28):

Here's a paper I saw posted on the arxiv yesterday. It's really cool! I haven't read through it in depth yet, but I think it's exciting. Does anyone have any observations/thoughts about it?

https://arxiv.org/abs/2405.04780

Brendan Murphy (May 10 2024 at 01:29):

As they say, it gives a sort of globular model for infinity categories. I wonder how the comonad here is related to the monad associated to the operad in the batanin definition of weak oo groupoids?

Josh Chen (May 10 2024 at 14:31):

Could you elaborate on which part gives a globular model for ∞-categories? From a quick skim I only see the claim for ∞-groupoids.

Brendan Murphy (May 10 2024 at 14:45):

Sorry, meant to say groupoids

Oscar Cunningham (May 10 2024 at 14:59):

So we can define an ∞-groupoid as a strict ∞-groupoid equipped with an ∞-functor to its 'strictification' obeying some axioms? Is there a concrete description of what the strictification functor does?

Brendan Murphy (May 10 2024 at 17:28):

I would say not really? It's constructed using a simplicial model on both sides, algebraic kan complexes and a full subcategory thereof where the distinguished horn fillers act like "thin" simplices. There's a procedure to collapse together pairs of simplices that "should be" the same in an algebraic kan complex if it were strict and strictification is defined as iterating this procedure ω times then taking a colimit. Very based on the presentation and not very conceptual imo