Homology of infinity-operads

Eric Hoffbeck; Ieke Moerdijk

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arXiv · 2105.11943

Homology of infinity-operads

Eric Hoffbeck·Ieke Moerdijk

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Abstract

In a first part of this paper, we introduce a homology theory for infinity-operads and for dendroidal spaces which extends the usual homology of differential graded operads defined in terms of the bar construction, and we prove some of its basic properties. In a second part, we define general bar and cobar constructions. These constructions send infinity-operads to infinity-cooperads and vice versa, and define an adjoint bar-cobar (or "Koszul") duality. Somewhat surprisingly, this duality is shown to hold much more generally between arbitrary presheaves and copresheaves on the category of trees defining infinity-operads. We emphasize that our methods are completely elementary and explicit.

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Eric Hoffbeck, Ieke Moerdijk. 2021-05-25. Homology of infinity-operads. https://arxiv.org/abs/2105.11943

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