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7h
comment Is the product of group representations commutative?
By product do you mean tensor product? If so, then yes.
1d
comment Homotopy Equivalence and Local Coefficient Systems
Local systems pull back along maps, so you use the pullback of the local system along a homotopy inverse of $f$.
1d
answered Is there something interesting about $373857714078$?
2d
comment Monomorphisms and injectivity predicates
@tcamps: well, if you don't require that $F$ is at least faithful then it need not reflect monomorphisms.
2d
comment Monomorphisms and injectivity predicates
@darij: I am confused about the precise phrasing of the question. I would have expected it to be what I said: "what are necessary and sufficient conditions for a class of monomorphisms in $C$ to be the class of monomorphisms that remain monomorphisms after applying a faithful functor $F : C \to D$?" I don't see the point of requiring that $F$ is wide.
2d
revised How to find the Galois group of a polynomial?
added 280 characters in body
2d
comment How to find the Galois group of a polynomial?
@Jim: yes, as azimut says I overlooked that $D_4$ also has a transposition in it...
Jun
27
comment How to prove this is a fibre bundle?
Have you tried applying Ehresmann's theorem?
Jun
27
comment Why is the codimension of an algebraic set defined by $r$ equations at most $r$?
If you know that the dimension of a variety is the generic value of the dimension of its Zariski tangent spaces, then this is clear: each equation reduces the dimension of the Zariski tangent space at a point by at most $1$.
Jun
26
accepted When is there a submersion from a sphere into a sphere?
Jun
26
answered How can I get a cohomology of hypersurfaces by using their equation?
Jun
25
comment Vanishing of the first Chern class of a complex vector bundle
Yes, this is true. Both conditions are equivalent to the condition that the top exterior power of $E$ is trivializable.
Jun
25
comment A “non-degenerate pairing” between $\operatorname{Gal}(K/k)$ and $K/k$
The general category-theoretic tool you want is called a Galois connection, which is a pair of adjoint functors between two posets. A nondegenerate bilinear pairing $V \otimes W \to \mathbb{R}$ induces a Galois connection between subspaces of $V$ and subspaces of $W$; similarly, the Galois correspondence induces a Galois connection between subgroups of the Galois group and subextensions of the Galois extension. In both cases the adjoint functors involved are contravariant.
Jun
24
awarded  Popular Question
Jun
24
awarded  Good Answer
Jun
24
comment Reduction to the special orthogonal group
That isn't what the first condition means. The first condition means that the transition functions can be taken to satisfy $\det g = 1$.
Jun
24
comment Closure of Set in Zariski Topology
Yes. This follows from chasing through the definition of the Zariski topology.
Jun
24
comment Why is $f(x)=x^{2}+1$ a primitive recursive function?
Can you show that addition and multiplication are primitive recursive, then conclude from there that the sum and product of two primitive recursive functions is primitive recursive?
Jun
23
comment Is there a “Coalgebra - Cogeometry” duality? Good opposite of a category of coalgebras?
If $R$ is a field, cocommutative coalgebras over $R$ are the ind-category of finite-dimensional cocommutative coalgebras over $R$, which is dual to the category of finite-dimensional commutative algebras over $R$; this is itself dual to a category of formal varieties, and hence the original category of coalgebras is a category of "ind-formal" varieties.
Jun
23
comment Is there a “Coalgebra - Cogeometry” duality? Good opposite of a category of coalgebras?
(Cocommutative) coalgebras are formal spaces. This is not a duality: the correspondence is covariant rather than contravariant.