Monoidal structures on triangulated fibered categories

Abstract

Let $\mathcal{S}$ be a small category admitting binary products. There exists a canonical dictionary expressing the structure and properties of monoidal $\mathcal{S}$-fibered categories in terms of the external tensor product in place of the usual internal tensor product. In this paper, we specialize this dictionary to the setting of triangulated $\mathcal{S}$-fibered categories, by studying how the general translation process interacts with shift functors. Our results provide a satisfactory abstract framework to study monoidal structures from the perspective of perverse sheaves.

arXiv comment37 pages; v2: revised introduction, some references added; v3: new title, structure of the paper modified (main results unchanged)

References in corpus (3)

• Triangulated categories of mixed motives
• The universal six-functor formalism
• Tensor structure on perverse Nori motives

Cited by in corpus (3)

• Tensor structure on perverse Nori motives
• On the functoriality of universal abelian factorizations
• Constructing monoidal structures on fibered categories via factorizations