Derivators, pointed derivators and stable derivators

By Moritz Groth. 2011

99 citations recorded by the source corpus.

We develop some aspects of the theory of derivators, pointed derivators and stable derivators. Stable derivators are shown to canonically take values in triangulated categories. Similarly, the functors belonging to a stable derivator are canonically exact so that stable derivators are an enhancement of triangulated categories. We also establish a similar result for additive derivators in the context of pretriangulated categories. Along the way, we simplify the notion of a pointed derivator, reformulate the base change axiom and give a new proof that a combinatorial model category has an underlying derivator. 55U35, 55U40, 55PXX

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d54d4a2ca3644eb33a5394fe5f7b5354e56c2389

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Support theory via actions of tensor triangulated categories (2011, methodology): “t Kan extensions along the smallest full 2-subcategory of the category of small categories satisfying certain natural closure conditions and containing the ordinals (one can see the discussion before [23] Deﬁnition 4.21 for further details). We begin by showing that, when T has a model, taking the u”
On compactly generated torsion pairs and the classification of co--structures for commutative noetherian rings (2012, background): “ in [25]. This diﬀerence is inessential but one should keep it in mind. We will stick to the majority convention that the direction of 2-morphisms is inverted as well. When referring to statements in [25], we will always mean their appropriately dualized versions. 8 JAN ˇSTOVˇ ´ICEK AND DAVID POSPˇ ”
Derived equivalences induced by big cotilting modules (2013, background): “tegory Gsatisﬁes more properties. We have not reﬂected yet that all the categories DG(I) are triangulated (and in particular additive). This leads to the notion of a stable derivator. Deﬁnition 5.11 ([Gro13]). A derivator Dis pointed if: (Der6) The categoryD(1) is a pointed category(i.e. the initial”