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1d
comment What is Equipotent relation?
These are good questions, but they are off-topic for this site.
1d
comment What is the algebraic role of the mathematical constant $\gamma$?
It all depends what you mean by "algebraic", then.
1d
comment What is the algebraic role of the mathematical constant $\gamma$?
It sounds like the question is trying to ask what identities (equations) are there in which $\gamma$ appears. Of course it does figure a lot in the theory of the $\Gamma$ function.
1d
awarded  Good Question
1d
comment Does the Diophantine equation $(x^2+ay^2)(u^2+bv^2) = p^2+cq^2$ admit a complete solution?
I'll take it on faith that these do provide solutions. Whether they provide all solutions is left completely unclear.
2d
awarded  Nice Question
2d
comment Collecting proofs that finite multiplicative subgroups of fields are cyclic.
For what it might be worth, the nLab has a proof here: ncatlab.org/nlab/show/root+of+unity#over_a_field
Dec
24
answered Is certain topology-related set a distributive lattice?
Dec
24
comment Is certain topology-related set a distributive lattice?
@მამუკაჯიბლაძე I think I follow what you're saying, but there might be a slight sticking point in accounting for Victor's axiom 3. I'm going to reformulate some of it in a separate answer; I'd be obliged if you'd have a look.
Dec
23
comment Cantor's theorem for presheaves?
I don't consider the small category case interesting, since we can just consider constant presheaves which form an essentially large class.
Dec
22
answered Is every closed subgroup of dual group an annihilator?
Dec
22
comment How has modern algebraic geometry affected other areas of math?
Late to this party; have only just seen this thread. I get the impression that your friend thinks polynomials are grubby, low-level things. I'd say he should think of polynomials are precisely the definable operations in ring theory (he likes non-commutative geometry? he probably doesn't hate rings then). Equivalently, polynomials are what constitute free algebras. Classical AG is then the study of the structure of definable sets for a singularly important algebraic theory.
Dec
22
accepted Cantor's theorem for presheaves?
Dec
22
comment Cantor's theorem for presheaves?
Ah, your more recent proof is both easier to follow and more general. I'm accepting this answer.
Dec
22
comment Tensor product over a monoid in a monoidal category
No particular reference comes to mind, although this type of construction is a basic tool in category theory. Suitably abstracted, for example, this construction yields relatively free algebras (see e.g. the discussion here: ncatlab.org/nlab/show/…), and appears as a canonical augmentation in two-sided bar constructions. You can find some related discussion here: mathoverflow.net/questions/180673/…
Dec
22
comment Cantor's theorem for presheaves?
Beautiful! The intuition coming from simplicial sets is very helpful as well. +1 for now as I wait to see if anyone else wants to answer. Something about the focus on retractions is stylistically reminiscent of the Freyd-Street paper as well.
Dec
21
comment Cantor's theorem for presheaves?
@QiaochuYuan I am happy to use universes to assume that $Set$ and $C$, $C^{op}$ are small relative to the universe and small categories in that universe form something cartesian closed as a 1-category. (In other words, I am happy to work in a cartesian closed pretopos where we assume the existence of an internal topos object $S$.) But I don't see how you can really implement the rest of Lawvere's diagonalization argument, because of the issue of the opposite variance noted towards the end of my post.
Dec
21
comment Cantor's theorem for presheaves?
With Andrej, I also favor the Lawvere fixed-point theorem POV, which is why I linked to Yanofsky's paper (where I mentioned diagonalization).
Dec
21
awarded  Nice Question
Dec
21
asked Cantor's theorem for presheaves?