The homotopy colimit of an $\infty$-local system as a twisted tensor product

Manuel Rivera, Mahmoud Zeinalian

Published 2018-05-03Version 1

We describe several equivalent models for the $\infty$-category of $\infty$-local systems of chain complexes using the framework of quasi-categories. We prove one of these equivalences exploiting the relationship between the differential graded nerve and the cobar functor. Then we use one of the models to calculate the homotopy colimit of an $\infty$-local system in terms of a twisted tensor product.