#homotopy — Public Fediverse posts

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

Can you define a 'simplicial set of small simplicial sets' by defining Δⁿ → Simp to be the set of small simplicial sets over Δⁿ, i.e. A → Δⁿ?

Would we then have that the maps B → Simp were in correspondence with the simplicial sets over B, for all B?

#CategoryTheory #SimplicialSets #Homotopy

I have neglected this channel, sorry lol. If you follow me you will probably find this interesting: https://arxiv.org/abs/2307.00442

#categories #homotopy #motives #gaugetheory #QFT

Today I got to have the full #intuitionist #constructivist #maths experience.

First, somebody half-jokes that if one is a constructivist, then one's friends won't talk to them anymore.

Then, somebody else says that #constructivism is a deviant counterculture.

At this point, like a fool, I link Bauer's "five stages" paper: https://www.ams.org/journals/bull/2017-54-03/S0273-0979-2016-01556-4/S0273-0979-2016-01556-4.pdf

But alas, somebody actually reads the paper, and they think that the whole paper is a joke. They have two concrete questions, which I answer using relevant examples.

This was all in the context of #homotopy #TypeTheory, for what it's worth.