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 ...

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 ...

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 ...

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 ...

2
votes

Accepted

### Completeness of comma $\infty$-categories

I think that this is proved in [Nikolausâ€“Scholze, On topological cyclic homology] Prop II.1.5.

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) ...

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....

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....

Only top scored, non community-wiki answers of a minimum length are eligible

#### Related Tags

higher-category-theory × 1294ct.category-theory × 815

homotopy-theory × 251

infinity-categories × 222

at.algebraic-topology × 175

simplicial-stuff × 133

model-categories × 105

reference-request × 103

higher-algebra × 90

topos-theory × 73

infinity-topos-theory × 69

ag.algebraic-geometry × 66

2-categories × 52

monoidal-categories × 42

homological-algebra × 38

limits-and-colimits × 30

stable-homotopy × 29

stacks × 29

topological-quantum-field-theory × 28

derived-algebraic-geometry × 28

operads × 25

enriched-category-theory × 25

derived-categories × 23

simplicial-categories × 21

extended-tqft × 19