The codual quotient vector bundle

Abstract

Given a quotient vector bundle $\mathcal{A}$ over $X$ with kernel map $\kappa :X\to \mathrm{Max}A$ we study the codual bundle with fiber at each point $x\in X$ isomorphic to the dual of $\kappa (x)$. Applying the adjunction between quotient vector bundles and linearized locales to the codual bundle leads to a new adjunction between the category of all quotient vector bundles and a category whose objects are locales $L$ equipped with a contravariant morphism $L\to \mathrm{Max}A$.