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arXiv · 2605.22418

The inflation functor in pluripotential homological algebra

Pedro Magalhães·Anna Sopena-Gilboy
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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.

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Pedro Magalhães, Anna Sopena-Gilboy. 2026-05-21. The inflation functor in pluripotential homological algebra. https://arxiv.org/abs/2605.22418

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