Derived categories for Grothendieck categories of enriched functors

2018/03/26 by Garkusha, Grigory, Jones, Darren
#Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1803.09451

Abstract

The derived category D[C,V] of the Grothendieck category of enriched functors [C,V], where V is a closed symmetric monoidal Grothendieck category and C is a small V-category, is studied. We prove that if the derived category D(V) of V is a compactly generated triangulated category with certain reasonable assumptions on compact generators or K-injective resolutions, then the derived category D[C,V] is also compactly generated triangulated. Moreover, an explicit description of these generators is given.

Related

• Grothendieck enriched categories
• The Grothendieck Construction and Gradings for Enriched Categories
• The derived category with respect to a generator
• A note on the definition of derived functors
• Six operations on dg enhancements of derived categories of sheaves