Justin Curry
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Registered User
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I am a second-year grad student.
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Mar 20 |
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Cosheafification @arsmath: Yes, you are right. It has a pretty strong consistency requirement. If I understand correctly, the strength of Vopenka's principle lies between Reinhardt cardinals and unmeasurable cardinals, but I don't have any committed opinions as to how controversial this is. I tend not to worry too much about these things, but perhaps I should. |
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Mar 20 |
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Cosheafification Nice! Does this proof assume Vopenka's principle? |
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Mar 20 |
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Cosheafification @Ryan: No, a functor $F:C\to D$ always can be used formally to define a functor $F^{op}:C^{op}\to D^{op}$. The assignment of objects remains the same, so $F^{op}(x)=F(x)$, but now a morphism $f:x\to y$ in $C$ becomes a morphism $f^{op}:y\to x$. The functor $F^{op}$ sends $f^{op}$ to $F(f)^{op}$. $F(f):F(x)\to F(y)$ defines a morphism $F(f)^{op}:F(y)\to F(x)$ in $D^{op}$, which is equal to $F^{op}(f^{op}):F^{op}(y)\to F^{op}(x)$. I don't know what you mean by "destroys covers." |
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Mar 19 |
revised |
Cosheafification added 1 characters in body |
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Mar 19 |
answered | Cosheafification |
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Jan 20 |
awarded | ● Necromancer |
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Jan 20 |
answered | Cosheaf homology and a theorem of Beilinson (in a paper on Mixed Tate Motives) |
