From 0303c4e1a700f6c5617f505a56cae88673a869da Mon Sep 17 00:00:00 2001 From: Viktor Kleen Date: Fri, 6 Mar 2015 20:56:31 +0000 Subject: more torsors --- lists/torsors/001 | 1 + lists/torsors/title | 1 + posts/torsors.md | 2 +- 3 files changed, 3 insertions(+), 1 deletion(-) create mode 120000 lists/torsors/001 create mode 100644 lists/torsors/title diff --git a/lists/torsors/001 b/lists/torsors/001 new file mode 120000 index 0000000..69340df --- /dev/null +++ b/lists/torsors/001 @@ -0,0 +1 @@ +../../posts/torsors.md \ No newline at end of file diff --git a/lists/torsors/title b/lists/torsors/title new file mode 100644 index 0000000..3597b97 --- /dev/null +++ b/lists/torsors/title @@ -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 $$(G\times U)\times_U (X\times U) \iso (X\times U) \times_U (X\times U)$$ and $(G\times U)\times_U(X\times U) = (G\times X)\times U$ and $(X\times -U)\times_U (X\times U)$ because pullback preserves products. So, $G\times X\to +U)\times_U (X\times U) = (X\times X)\times U$ because pullback preserves products. So, $G\times X\to X\times X$ is a local isomorphism, hence an isomorphism. [^1]: Saunders Mac Lane, Ieke Moerdijk. Sheaves in geometry and logic. Springer, 1994. ISBN: 0-387-97710-4 -- cgit v1.2.3