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Nov
14
comment Cech cohomology and cohomology of a category : a cluster of questions.
It's not that simple. Your definitions are not quite standard/correct. But it's basically correct.
Nov
13
comment Cech cohomology and cohomology of a category : a cluster of questions.
You can define Čech cohomology in terms of $\mathrm{Ext}$ of presheaves, and it is indeed linked to the fact that a covering gives rise to a free resolution. Some of the details are discussed here.
Nov
13
comment If $\{id_V, T, T^2, \ldots, T^d\}$ is linearly independent, then $d<r$.
If you know that the minimal polynomial is of that form then you know that $\{ \mathrm{id}_V, T, T^2, \ldots, T^r \}$ is not linearly independent. But that's a big if.
Nov
13
comment algebraic $1$-forms vs analytic $1$-forms
The algebraic counterpart of meromorphic 1-forms are elements of the stalk of the sheaf of algebraic 1-forms at the generic point.
Nov
13
revised Prove associative of $(A \setminus B)\cup C = A \setminus (B \cup C)$
edited tags
Nov
12
comment Refrence request for 2-categories
You could have a look at A 2-categories companion, but it isn't quite as complete as one might like.
Nov
12
comment Trying to understand the equivalence of two definitions of a sieve.
That is true when the components are in a category where kernel pairs exist.
Nov
12
comment Trying to understand the equivalence of two definitions of a sieve.
Actually, here it is best to use subpresheaf in the strictest possible sense: each $S A$ is a subset of $\mathcal{C}(A, C)$ and each map $S A \to \mathcal{C}(A, C)$ is the inclusion.
Nov
11
asked The projective model structure on chain complexes
Nov
11
comment Affine algebraic curve is Riemann surface
No, what you have done is not enough – unless you have proved the holomorphic version of the regular value theorem. A separate argument is needed for connectedness.
Nov
11
comment Affine algebraic curve is Riemann surface
The (holomorphic) inverse function theorem can be used to establish a holomorphic atlas on $X$, just as in the smooth case.
Nov
11
comment Generic Points to the Italians
Most likely, a generic point was literally just an arbitrary point drawn from a dense open subset, or something thereabouts.
Nov
11
comment A (too?) simple argument for the undefinability of definable sets
The suggested proof cannot work: while there are only countably many formulae, this can only be seen in the metatheory.
Nov
11
answered Do pushouts exist in a cartesian closed category?
Nov
11
comment Do pushouts exist in a cartesian closed category?
@MaliceVidrine Of course completeness is not automatic. Look at $\mathbf{FinSet}$.
Nov
11
comment Help in a proof in basic Algebraic Geometry
Well, it's true for all $g$. So it's true for $s_i$ as well.
Nov
11
revised Functions with the domain having greater cardinality than $\aleph_1$
edited tags
Nov
10
comment Formulas in a Field and in a Field Extension.
Well, (1) involves a non-linear equation but (2) does not. This heuristic is not foolproof but is a good starting point.
Nov
10
comment Is there anything to be learned from the spectrum of a cohomology ring?
$H^* (X)$ is not always a commutative ring, so how do you propose to apply $\operatorname{Spec}$ or $\operatorname{Proj}$ to it?
Nov
10
comment Can we define the homology of the homology chain complex
Of course you can make any sequence of modules into a chain complex: set $d = 0$.