Definition 19.7.8. The cosimplicial topological space \([n]\mapsto \abs {\Delta ^n}\) and pullback of vector bundles determine a simplicial object \[ [n]\longmapsto \Vect ^{\disc }(X\times \abs {\Delta ^n})^{\simeq } \] in \(\CRig (\An )\). We define the moduli anima of complex vector bundles over \(X\) by \[ \Vect (X)^{\simeq } := \colim _{[n]\in \simp \catop } \Vect ^{\disc }(X\times \abs {\Delta ^n})^{\simeq } \qin \CRig (\An ). \]
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