14 votes

Why do we say IndCoh(X) is analogous to the set of distributions on X?

The connection is perhaps a bit more clear if you think about the corresponding $\infty$-categories of compact objects: the claim is that coherent sheaves behave like distributions while perfect ...
G. Stefanich's user avatar
11 votes
Accepted

Can you deduce the correspondence between 2D oriented TQFTs and commutative Frobenius algebras from the (framed) Cobordism Hypothesis?

It turns our the most serious disparity is your first bullet point, not the second: the key difference is that the cobordism hypothesis is about fully extended TFT. A sub-issue is that in the fully ...
Adrien's user avatar
  • 8,232
6 votes
Accepted

Soft question: Deep learning and higher categories

Sure, there are plenty of potential applications of higher category theory to machine learning and deep learning. Such applications are still in their infancy, so don't expect a new algorithm, getting ...
David White's user avatar
  • 27.7k
5 votes

Soft question: Deep learning and higher categories

After the success of Graph Deep Learning, folks are moving up the chain: a few articles, see for instance this one, have begun considering Simplicial Neural Architectures (SSN) (the main motivation ...
Mirco A. Mannucci's user avatar
2 votes
Accepted

Completeness of comma $\infty$-categories

I think that this is proved in [Nikolaus–Scholze, On topological cyclic homology] Prop II.1.5.
Z. M's user avatar
  • 1,898
1 vote

Does the Gray tensor product exhibit Gray as a monoidal Gray-category?

If $V$ is a symmetric (or at least braided) monoidal closed category then there is a natural tensor product on the category of $V$-enriched categories. A $V$-enriched monoidal category is a (weak) ...
Tim Campion's user avatar
  • 60.2k
1 vote

Finitely presentable objects in the categories of algebras of $\infty$-algebraic theories

No, this fails even for the infinity category of spaces, where "free" means "discrete". A coequalizer of free spaces is a wedge of circles, so for example $S^2$ is not of this form....
Tim Campion's user avatar
  • 60.2k
1 vote

Explicit left adjoint to forgetful functor from Cartesian to symmetric monoidal categories

Here I conjecture an answer to the question above. I describe a tensor product of symmetric monoidal categories, which I claim makes the 2-category $\mathrm{SMC}$ into a symmetric monoidal 2-category....
John Baez's user avatar
  • 21.1k

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