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arXiv · 1803.01376

Homotopy Theory of linear coalgebras

Brice Le Grignou·Damien Lejay
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Abstract

We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full theory of coalgebras: with counits and not necessarily locally conilpotent. For example $\mathcal E_\infty$-coalgebras, $\mathcal A_\infty$-coalgebras, $\mathcal L_\infty$-coalgebras etc. To do so, we define the category of complete curved algebras -- where the notion of quasi-isomorphims does not make sense -- and endow it with a model category structure, equivalent to that of the category of coalgebras.

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Brice Le Grignou, Damien Lejay. 2018-03-04. Homotopy Theory of linear coalgebras. https://arxiv.org/abs/1803.01376

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