What is an equivalence in a higher category?
http://arxiv.org/abs/2303.00567
#arXiv_2303_00567
Axioms for the category of sets and relations
http://arxiv.org/abs/2302.14153
#arXiv_2302_14153
They just don't stop! Besides their Joy of Abstraction book club, the Topos Institute also has *another* way for you to start learning category theory.
It's called the CT Outreach Panel, and it's happening on March 16, 17:00 UTC.
Some of the best explainers of category theory in the world - Emily Riehl, Eugenia Cheng, Tai-Danae Bradley, Paul Dancstep and Oliver Lugg - will explain their approaches to the subject and answer questions.
You can submit questions here:
This post by @johncarlosbaez about rig categories is great!
https://mathstodon.xyz/@johncarlosbaez/109801982980939381
It got me thinking about my favorite example that's not exactly FinSet. It's a rig category Z whose objects are integers. Its only morphisms are automorphisms, and each automorphism group is ℤ/2 = {±1}. Even though addition of integers is commutative, the symmetry isomorphism in Z is nontrivial! The symmetry isomorphism
β: m + n ≅ n + m
is the element (-1)ᵐⁿ in Z(m+n,m+n).
(1/5)
finally found a journal for my expository paper on (co)simplicial (co)presheaves! first solo publication to actually appear (one of my thesis ones was accepted a couple of months ago but seems to be stuck in academic publication limbo)
@mathmathniconico
これはどうもありがとうございます。あの見方は、結局米田埋め込みが極限を保つから、極限に対しては集合論的に扱えるという話になります。そう考えると、圏論の基本を学んだときにすでに出会っているはずのものなのですが、Leinsterの文章を読むまで気づかないものですね…
京大理→阪大D2 / 圏論 / 代数幾何 /
Twitter:
https://twitter.com/paper3510mm