The inflation functor in pluripotential homological algebra
Algebraic Topology
2026-05-22 v1
Abstract
We introduce a functor from cochain complexes to bicomplexes, called inflation functor, which sends quasi-isomorphisms to the class of pluripotential weak equivalences. We show this functor is part of a Quillen adjunction. Its right adjoint is a well-known construction in complex geometry, which gives a sheaf-theoretic presentation of Bott-Chern and Aeppli cohomologies. The inflation functor plays a key role in pluripotential Koszul duality theory for operads and allows us to construct the infinity-category of bicomplexes in the pluripotential sense.
Cite
@article{arxiv.2605.22418,
title = {The inflation functor in pluripotential homological algebra},
author = {Pedro Magalhães and Anna Sopena-Gilboy},
journal= {arXiv preprint arXiv:2605.22418},
year = {2026}
}