Timeline for Do inverse images respect flabby sheaves?
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| Oct 10, 2011 at 20:31 | comment | added | Alex | The only thing I can say right now is that the result you want is not general nonsense, i.e. it is not a general property of topoi. In general, the functors that conserve flabby sheaves are $u_*$ ($u$ any morphism of topoi) and $i^!$ ($i$ a closed embedding), cf SGA 4 V 4.9 and 4.11. | |
| Oct 9, 2011 at 21:21 | comment | added | algori | At least in topology the corresponding statement is true when $Y$ has a fundamental system of paracompact neighborhoods. See Godement, chapter II, \S 3.3. In particular, if $X$ is metrizable (which is the case in most situations) the restriction of a flabby sheaf to any subspace of $X$ is flabby (ibid, corollary 2). | |
| Oct 9, 2011 at 20:49 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
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| Oct 9, 2011 at 20:19 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
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| Oct 9, 2011 at 20:13 | history | asked | Mikhail Bondarko | CC BY-SA 3.0 |