meta.mathoverflow.net/questions/4200/flood-of-similar-new-us‌​ers

meta.mathoverflow.net/questions/4200/flood-of-similar-new-us‌​ers

meta.mathoverflow.net/questions/4200/flood-of-similar-new-us‌​ers

@Gro-Tsen Ah, but the great thing about pseudotopological spaces is not in and of themselves, but their organization into a category that is a quasitopos: ncatlab.org/nlab/show/pseudotopological+space. To my mind this is their real raison d'être. See also "the dichotomy between nice objects and nice categories" ncatlab.org/nlab/show/….

This doesn't really look like homework. But generally it would be better to avoid the imperative mode when posting questions.

Polish spaces as another class?

Well, it is an isthmus. And if so, it seems to me that has only to do with finite generation of the Boolean ring, i.e., if algebraic geometers feel that way, then perhaps on similar grounds they are not so interested in spectra of infinitely generated algebras. (Is that true? I'm not sure.)

Stone spaces are Zariski spectra of Boolean rings.

(There is no problem as far as I can tell.)

meta.mathoverflow.net/questions/4200/flood-of-similar-new-us‌​ers

@user64494 Your earlier comment linked to the Ukrainian Wikipedia here uk.wikipedia.org/wiki/Magma where the article -- correct me if I'm wrong -- seems to be about a progressive rock group named MAGMA. In any case, a cursory examination of this site shows many users spelling the name of the algebra software as MAGMA, and therefore I find your edit of the orthography unnecessary. At a user's request, I am rolling back.

meta.mathoverflow.net/questions/4200/flood-of-similar-new-us‌​ers

meta.mathoverflow.net/questions/4200/flood-of-similar-new-us‌​ers

Naturality in the arguments $G$ and $H$ follows the well-known definition (compatibility between the isomorphism $\phi_{G, H}: F(G \times H) \to F(G) \otimes F(H)$ and morphisms $G \to G', H \to H'$ as expressed in the form of commutative squares). For further "coherence conditions", see ncatlab.org/nlab/show/monoidal+functor and ncatlab.org/nlab/show/symmetric+monoidal+functor, which include consideration of not just the monoidal products but also the monoidal units $1, \mathbb{Z}$. By the way, don't you mean to replace "on" with "to" in the question?

I feel this question could stand more structure. First, let's use an isomorphism $\cong$ in place of an equality; otherwise it's hard to make sense of the question. Then: should the isomorphism be natural? Should we be demanding more than mere naturality: should the isomorphism get along (be compatible) with associativity or symmetry isomorphisms? Do you care only about existence of an isomorphism (that satisfies to-be-specified properties), or should the choice of isomorphism be part of the structure considered? Etc.

@cardinal math.stackexchange.com/questions/1633326/…