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May 14 |
awarded | Caucus |
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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? |
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Apr 11 |
accepted | Symplectic Forms |
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Apr 11 |
asked | Symplectic Forms |
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Feb 25 |
comment |
Long Exact Sequence on Homology in an Abelian Category @Martin - why would that show it? |
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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? |
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Feb 23 |
asked | Long Exact Sequence on Homology in an Abelian Category |
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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 |
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Feb 1 |
awarded | Yearling |
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Jan 14 |
comment |
If an abelian category has a generator then it is well-powered Middle of this page: books.google.co.uk/… |
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Jan 14 |
accepted | If an abelian category has a generator then it is well-powered |
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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 |
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Jan 14 |
asked | If an abelian category has a generator then it is well-powered |
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Jan 14 |
accepted | Exactness of Colimits |
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Jan 4 |
accepted | Is $(gf)(X) = g ( f(X))$ in a category? |
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Dec 24 |
comment |
Exactness of Colimits unless $\bigoplus $ is sometimes used as a symbol for colimit? |
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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 |
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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? |
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Dec 24 |
asked | Exactness of Colimits |
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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 |
