(see also Chern-Weil theory, parameterized homotopy theory)
Given a bundle , and a morphism , then the pullback bundle is (if it exists) simply the pullback of along , regarded as a bundle over .
Over a paracompact topological space every vector bundle is isomorphic to a pullback bundle of a universal vector bundle over a classifying space. See there for more.
Notions of pullback:
pullback, fiber product (limit over a cospan)
lax pullback, comma object (lax limit over a cospan)
(∞,1)-pullback, homotopy pullback, ((∞,1)-limit over a cospan)
Last revised on December 2, 2020 at 12:30:39. See the history of this page for a list of all contributions to it.