Tensor product of A_∞-categories

2024/11/15 by Ornaghi, Mattia · 1 citation
#14F08 #18E35 #18G70 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.10300

Abstract

In this paper we define the tensor product of two A_∞-categories and two A_∞-functors. This tensor product makes the category of A_∞-categories symmetric monoidal (up to homotopy), and the category A_∞Cat^u/_≈ a closed symmetric monoidal category. Moreover, we define the derived tensor product making Ho(A_∞Cat), the homotopy category of the A_∞-categories, a closed symmetric monoidal category. We provide also an explicit description of the internal homs in terms of A_∞- functors.

Cited by

• A model structure on the category of A_∞-categories with strict morphisms

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