Timeline for Is the category of vector bundles over a topological space abelian?

6 events

when toggle format	what		by	license	comment
Sep 13, 2012 at 16:25	history	undeleted	Ryan Reich
Sep 13, 2012 at 16:25	history	edited	Ryan Reich	CC BY-SA 3.0	added 11 characters in body
Sep 13, 2012 at 16:23	history	deleted	Ryan Reich
Sep 13, 2012 at 16:15	comment	added	Damian Rössler		View $\bf R$ (resp. ${\bf R}^2$) as the trivial (real) vector bundle of rank $1$ (resp. rank $2$) over the real line $\bf R$, viewed as a topological space with the ordinary topology. Let $f:{\bf R}\to {\bf R}^2$ be the map of vector bundles st $f(t,v)=(t,v\cdot(t,1))$. Let $g:{\bf R}^2\to{\bf R}$ be the map of vector bundles $g(t,v,w)=(t,v)$. Then $g$ and $f$ have constant rank but $g\circ f$ does not (because $g\circ f$ restricted to $0$ as rank $0$ and not otherwise). So the class you describe is not a category.
Sep 13, 2012 at 16:11	comment	added	Laurent Moret-Bailly		Unfortunately, the second category is not additive.
Sep 13, 2012 at 15:37	history	answered	Ryan Reich	CC BY-SA 3.0