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 Yearling
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May
14
awarded  Caucus
Apr
11
comment Symplectic Forms
Sorry I'm a bit confused. We have that $\omega \wedge \ldots \wedge \omega$ at $x$ is an alternating multilinear map $T_x M \times \ldots T_x M \longrightarrow \mathbb R$. In what sense is this map just $\operatorname{det}\omega_x$ and how do I see it?
Apr
11
accepted Symplectic Forms
Apr
11
asked Symplectic Forms
Feb
25
comment Long Exact Sequence on Homology in an Abelian Category
@Martin - why would that show it?
Feb
24
comment Long Exact Sequence on Homology in an Abelian Category
OK ill check out CWM. From what I understand the embedding theorem holds for small abelian categories - does it hold in general?
Feb
23
asked Long Exact Sequence on Homology in an Abelian Category
Feb
19
comment Why do we accept Kuratowski's definition of ordered pairs?
it's just probably the nicest way to encode that required property that you wrote
Feb
1
awarded  Yearling
Jan
14
comment If an abelian category has a generator then it is well-powered
Middle of this page: books.google.co.uk/…
Jan
14
accepted If an abelian category has a generator then it is well-powered
Jan
14
comment If an abelian category has a generator then it is well-powered
Is it true that a Grothendieck category always has a strong generator? I'm just asking because I am sure I read somewhere that a Grothendieck category is always well-powered
Jan
14
asked If an abelian category has a generator then it is well-powered
Jan
14
accepted Exactness of Colimits
Jan
4
accepted Is $(gf)(X) = g ( f(X))$ in a category?
Dec
24
comment Exactness of Colimits
unless $\bigoplus $ is sometimes used as a symbol for colimit?
Dec
24
comment Tensor product and exterior algebra
For your first question define a bilinear map on M x N and use the universal property of the tensor product. This will give you a linear map on the tensor product. You can similarly define a bilinear map on N x M which will give a linear map on the tensor product. You can check they are inverses. To define maps on tensor products, as a matter of course you should define bilinear maps on M x N and then use the UP
Dec
24
comment Exactness of Colimits
@Mariano perhaps this should have been emphasised in the source. However in the source it is asserted that the other two colimits are just in fact coproducts. Is it true that we get the coproduct when we take the colimit of $ X_\bullet $and $ X / X_\bullet $ if $ I $ is directed/filtered?
Dec
24
asked Exactness of Colimits
Dec
20
comment Is $(gf)(X) = g ( f(X))$ in a category?
@ZhenLin Could you explain why having pullbacks means that the images compose? I am having trouble seeing it. Thanks a lot