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Aug
17
comment Cech Cohomology and the Dold-Kan Correspondence
If you have an open cover you can get a simplicial object.
Aug
16
comment Is the Quillen Injective Model Structure on the category of positive cochain complexes of R-modules (co)fibrantly generated?
I think the answer is yes, but it may be difficult to get an explicit generating set of trivial cofibrations. The key phrase is "Smith's theorem".
Aug
16
revised Is the Quillen Injective Model Structure on the category of positive cochain complexes of R-modules (co)fibrantly generated?
edited tags
Aug
16
comment Intuition for homotopy (co)limits in triangulated categories
The analogue to think about is an abelian category with countable coproducts. How would you construct colimits for sequences using use coproducts and cokernels?
Aug
15
comment Left adjoint of the forgetful functor $\mathsf{Grpd} \to \mathsf{Cat}$?
Yes, the left adjoint exists. The morphisms are zigzags, as you say.
Aug
15
comment Is the reflective localization $L_WC$ of a category $C$ equivalent to $C$? What am I missing?
Sometimes functors are not the obvious ones.
Aug
14
comment Why is $\mathsf{Type} : \mathsf{Type}$ a contradiction?
No, it is not a matter of notation. Girard's paradox is more like the Burali-Forti paradox.
Aug
14
comment Replacing a covering in a site with a single arrow
The answer is essentially contained here
Aug
14
comment Is any splitting field algebraic?
Actually, $K[X] / (f)$ may not be a splitting field for $f$.
Aug
14
comment Why is $\mathsf{Type} : \mathsf{Type}$ a contradiction?
@user40276 No. This is Girard's paradox.
Aug
13
comment Is the parametrization $(t^3,t^6)$, a reparametrization of $(t,t^2)$?
Well, then you don't have a reparametrisation, because the inverse is not smooth.
Aug
13
comment Is the parametrization $(t^3,t^6)$, a reparametrization of $(t,t^2)$?
Obviously that theorem depends on the definition of "reparametrisation".
Aug
13
answered Is this assignment of the topos of sheaves functorial?
Aug
12
comment degree of an etale cover of the affine line
If $X \to \mathbb{A}^1_k$ is a finite étale cover and $X$ is connected then it is an isomorphism. No? For $k = \mathbb{C}$ this corresponds to the fact that $\mathbb{C}$ is simply connected.
Aug
11
comment Choosing projective replacement to be functorial
1. Classical derived functors are functors – between the derived categories. 2. Look up Cartan–Eilenberg resolutions. 3. A functorial projective replacement should be enough. 4. There is only one possible meaning.
Aug
11
comment Can you integrate on a scheme?
Integrate what?
Aug
11
comment Derived functors definition
That is the assumption, yes. Please read carefully.
Aug
10
comment Sifted colimits of models of a Lawvere theory.
I'm not so certain that filtered colimits + reflexive coequalisers suffice for all sifted colimits, but at any rate the conclusion about finitary monads on $\mathbf{Set}$ is correct. It's less clear to me what happens for monads of higher accessibility rank, though.
Aug
10
comment Examples of preadditive categories
The total category of modules is not preadditive.
Aug
10
awarded  Enlightened