2 problems

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A Serre–Swan conjecture relating higher vector bundles and abstract representations up to homotopy
A higher vector bundle is intended to correspond to an abstract representation up to homotopy (ruth), namely a finitely generated projective right graded $CG$ -module equipped with…
Conjectureopenhigher-vector-bundles representations-up-to-homotopy serre-swan-theoremarXiv posted 2 days ago
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Invariance of representations up to homotopy under Lie algebroid n-equivalence
Invariance conjecture. There is an equivalence of categories between representations up to homotopy of length at most $n$ of $A$ and of $B$ .
Conjectureopenlie-algebroids representations-up-to-homotopyarXiv posted 2 days ago

A Serre–Swan conjecture relating higher vector bundles and abstract representations up to homotopy