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arXiv · 1903.01639

A recurrent formula of $A_{\infty}$-quasi inverses of dg-natural transformations between dg-lifts of derived functors

Zhaoting Wei
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Abstract

A dg-natural transformation between dg-functors is called an objectwise homotopy equivalence if its induced morphism on each object admits a homotopy inverse. In general an objectwise homotopy equivalence does not have a dg-inverse but has an $A_{\infty}$ quasi-inverse. In this note we give a recurrent formula of the $A_{\infty}$ quasi-inverse. This result is useful in studying the compositions of dg-lifts of derived functors of schemes.

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Zhaoting Wei. 2019-03-05. A recurrent formula of $A_{\infty}$-quasi inverses of dg-natural transformations between dg-lifts of derived functors. https://arxiv.org/abs/1903.01639

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