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Apr
21
comment French translation of “well-powered” category
@Pece In SGA 4 they seem to just say ‘l'ensemble des sous-objets de $X$ dans $C$ est petit’...
Apr
21
comment French translation of “well-powered” category
@user42912 No, that refers to "full subcategories".
Apr
21
comment A locally constant sheaf on a locally connected space is a covering space; Proof?
Ah, they have a different definition... and a strange one at that. I suspect it doesn't work well in a non-Hausdorff space. Here is what I would use: a sheaf $\mathscr{F}$ is locally constant if there exists an open cover of the space such that the restriction of $\mathscr{F}$ to each open set in the cover is a constant sheaf.
Apr
21
comment A locally constant sheaf on a locally connected space is a covering space; Proof?
I don't think $\mathscr{F}$ is a locally constant sheaf: the restriction of $\mathscr{F}$ to $\{ a, b \}$ is not a constant sheaf.
Apr
20
answered Allegories in easy words?
Apr
20
answered When are these two definitions of “monomorphism” equivalent?
Apr
20
accepted What fragment of ZFC do we need to prove Zorn's lemma?
Apr
20
comment Every smooth cubic curve has a flex point
Is it really necessary to apply Bézout's theorem? There's a weak form that you can prove by hand that says that any two projective plane curves must intersect.
Apr
19
revised Showing image of an integral operator is continuous
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Apr
19
comment Any branch of math can be expressed within set theory, is the reverse true?
Well, if you are willing to climb up one level of abstraction, all of mathematics can be carried out in arithmetic: first formalise everything in ZFC, then formalise the formalisation in PA!
Apr
19
answered Are groups algebras over an operad?
Apr
19
comment Is it useful to view magmas as diagrams?
The data is a diagram, and the axiom is that the diagram commutes!
Apr
18
comment When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
If $M$ is finitely-generated and $N$ is noetherian, then $\textrm{Hom}_R (M, N)$ is also finitely-generated (indeed, noetherian).
Apr
18
comment Why is a variety etale locally like affine space?
I doubt it. Take $Y = \operatorname{Spec} k$ and $X = \mathbb{A}^2_k \setminus \{ (0, 0) \}$; then we must have $V = Y$ and $d = 2$. It's not clear to me where one would get a étale surjection $U \to \mathbb{A}^2_k$ where $U$ is an affine open subscheme of $X$.
Apr
18
comment Intuition behind the Axiom of Choice
@AsafKaragila I do think AC is a kind of local-to-global principle of the same kind as induction, however: it says, if I can make a choice locally (i.e. for each member of a set), then I can make a choice globally (i.e. for the whole set at once).
Apr
17
answered Algebraic description of a stalk in the fppf topology
Apr
17
revised explicitly represent a representable functor
added 1152 characters in body
Apr
17
comment explicitly represent a representable functor
Read the penultimate paragraph.
Apr
17
answered explicitly represent a representable functor
Apr
17
comment What analysis is needed for AG?
If you haven't done some differential geometry, then the notion of tangent space or smooth variety will probably be somewhat mysterious. But you don't need to know differential geometry, because the definitions in algebraic geometry are purely algebraic!