Virtual vector bundle

Definition 10.2.15 (Virtual vector bundle). Let \(A\) be an anima. A virtual vector bundle on \(A\) is a map of animae \[ V\colon A \longrightarrow \BOP . \] Its rank is the composite \(\rk (V)\colon A \to \Z \) with the projection to \(\Z \), and we say that \(V\) has rank \(d \in \Z \) if this composite is constant with value \(d\). A virtual vector bundle on a topological space \(X\) means one on \(\Pi _{\infty }(X)\).