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authorViktor Kleen <viktor@kleen.org>2015-03-06 20:56:31 +0000
committerViktor Kleen <viktor@kleen.org>2015-03-06 20:56:31 +0000
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parent94956f26a68f129a4d4076ad83498d38629ad609 (diff)
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more torsors
l---------lists/torsors/0011
-rw-r--r--lists/torsors/title1
-rw-r--r--posts/torsors.md2
3 files changed, 3 insertions, 1 deletions
diff --git a/lists/torsors/001 b/lists/torsors/001
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../../posts/torsors.md \ No newline at end of file
diff --git a/lists/torsors/title b/lists/torsors/title
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@@ -0,0 +1 @@
Torsor in Toposes
diff --git a/posts/torsors.md b/posts/torsors.md
index b87c2df..a4cab97 100644
--- a/posts/torsors.md
+++ b/posts/torsors.md
@@ -94,7 +94,7 @@ and transitive, so in $\ca C/U$ we have the isomorphism
94$$(G\times U)\times_U (X\times U) \iso (X\times U) 94$$(G\times U)\times_U (X\times U) \iso (X\times U)
95\times_U (X\times U)$$ 95\times_U (X\times U)$$
96and $(G\times U)\times_U(X\times U) = (G\times X)\times U$ and $(X\times 96and $(G\times U)\times_U(X\times U) = (G\times X)\times U$ and $(X\times
97U)\times_U (X\times U)$ because pullback preserves products. So, $G\times X\to 97U)\times_U (X\times U) = (X\times X)\times U$ because pullback preserves products. So, $G\times X\to
98X\times X$ is a local isomorphism, hence an isomorphism. 98X\times X$ is a local isomorphism, hence an isomorphism.
99 99
100[^1]: Saunders Mac Lane, Ieke Moerdijk. Sheaves in geometry and logic. Springer, 1994. ISBN: 0-387-97710-4 100[^1]: Saunders Mac Lane, Ieke Moerdijk. Sheaves in geometry and logic. Springer, 1994. ISBN: 0-387-97710-4