# Tensor products of representations up to homotopy

## Camilo Arias Abad, Marius Crainic and Benoit Dherin

We study the construction of tensor products of representations up to homotopy, which are the $A_\infty$ version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and of morphisms between them, and show that these formulas give the homotopy category a monoidal structure which is uniquely defined up to equivalence.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 2, pp. 239-288