107 research outputs found
-Structures on stable derivators and Grothendieck hearts
We prove that given any strong, stable derivator and a -structure on its
base triangulated category , the -structure canonically lifts to all
the (coherent) diagram categories and each incoherent diagram in the heart
uniquely lifts to a coherent one. We use this to show that the -structure
being compactly generated implies that the coaisle is closed under directed
homotopy colimit which in turns implies that the heart is an (Ab.) Abelian
category. If, moreover, is a well generated algebraic or topological
triangulated category, then the heart of any accessibly embedded (in
particular, compactly generated) -structure has a generator. As a
consequence, it follows that the heart of any compactly generated -structure
of a well generated algebraic or topological triangulated category is a
Grothendieck category.Comment: 47 page
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