Pushforward and smooth vector pseudo-bundles

Abstract

In this paper, we study a new operation named pushforward on diffeological vector pseudo-bundles, which is left adjoint to the pullback. We show how to pushforward projective diffeological vector pseudo-bundles to get projective diffeological vector spaces, producing many concrete new examples. This brings new objects to diffeology from classical vector bundle theory.

On the geometry of diffeological vector pseudo-bundles and infinite dimensional vector bundles: automorphisms, connections and covariant derivatives

“…Isomorphisms of vector pseudo-bundles. We now rephrase vector pseudobundle morphisms and isomorphisms described in [51] in a non-categorical vocabulary.…”

“…Remark 3.8. Following [51], if (φ, ϕ) ∈ Aut(E), then ϕ is the restriction of φ to the zero-section of E.…”