Homotopy units in 𝐴-infinity algebras

Muro, Fernando

doi:10.1090/tran/6545

Homotopy units in $A$-infinity algebras
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Trans. Amer. Math. Soc. 368 (2016), 2145-2184 Request permission

Abstract:

We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra structures on a given object is up to homotopy a subset of connected components of the space of non-unital associative algebra structures.

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