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Andrej Bauer
Andrej Bauer
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Faliure of Does the Čech cohomology always yield long exact sequence for Čehov cohomologysequences from short ones?

Does Čehovthe Čech cohomology ever fail toalways give rise to a long exaxtexact sequences given a short exact sequence of sheaves?

Clearly that can notcannot occur for sheaves on a paracomact (perhaps also Hausdorff, I'm not sure about that) spacesspace, but the argument one uses there relies on the topological assumptions in a crucial way and can notcannot be generalized to an arbitrary space, not in a straight-forward manner anyway.

Thank you for shedding any light on this issue!

Faliure of long exact sequence for Čehov cohomology?

Does Čehov cohomology ever fail to give rise to a long exaxt sequences given a short exact sequence of sheaves?

Clearly that can not occur for sheaves on paracomact (perhaps also Hausdorff, I'm not sure about that) spaces, but the argument one uses there relies on the topological assumptions in a crucial way and can not be generalized to an arbitrary space, not in a straight-forward manner anyway.

Thank you for shedding any light on this issue!

Does the Čech cohomology always yield long exact sequences from short ones?

Does the Čech cohomology always give rise to a long exact sequences given a short exact sequence of sheaves?

Clearly that cannot occur for sheaves on a paracomact (perhaps also Hausdorff, I'm not sure about that) space, but the argument one uses there relies on the topological assumptions in a crucial way and cannot be generalized to an arbitrary space, not in a straight-forward manner anyway.

Thank you for shedding any light on this issue!

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HeWhoHungers
HeWhoHungers
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Faliure of long exact sequence for Čehov cohomology?

Does Čehov cohomology ever fail to give rise to a long exaxt sequences given a short exact sequence of sheaves?

Clearly that can not occur for sheaves on paracomact (perhaps also Hausdorff, I'm not sure about that) spaces, but the argument one uses there relies on the topological assumptions in a crucial way and can not be generalized to an arbitrary space, not in a straight-forward manner anyway.

Thank you for shedding any light on this issue!