Corollary 19.7.10. The construction of Definition 19.7.8, applied to finite-rank real vector bundles, defines a functor \[ \Vect _{\R }(-)^{\simeq }\colon \Top \catop \longrightarrow \CRig (\An ) \] whose underlying anima is computed by the corresponding colimit in \(\An \).
Proof. The constructions and proofs of Proposition 19.7.6, Corollary 19.7.7, Proposition 19.7.9 apply verbatim with \(\C \) replaced by \(\R \). □
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