Revisiting the canonicity of canonical triangulations

Moritz Groth

Stable derivators provide an enhancement of triangulated categories as is indicated by the existence of canonical triangulations. In this paper we show that exact morphisms of stable derivators induce exact functors of canonical triangulations, and similarly for arbitrary natural transformations. This 2-categorical refinement also provides a uniqueness statement concerning canonical triangulations.

These results rely on a more careful study of morphisms of derivators and this study is of independent interest. We analyze the interaction of morphisms of derivators with limits, colimits, and Kan extensions, including a discussion of invariance and closure properties of the class of Kan extensions preserved by a fixed morphism.

Keywords: stable derivators, triangulated categories, exactness properties

2010 MSC: 55U35, 18G55

Theory and Applications of Categories, Vol. 33, 2018, No. 14, pp 350-389.

Published 2018-05-01.

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