Geodesic
Revisiting the canonicity of canonical triangulations
Theory and applications of categories, Tome 33 (2018), pp. 350-389.

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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.
Publié le :
Classification : 55U35, 18G55
Keywords: stable derivators, triangulated categories, exactness properties 
@article{TAC_2018_33_a13,
     author = {Moritz Groth},
     title = {Revisiting the canonicity of canonical triangulations},
     journal = {Theory and applications of categories},
     pages = {350--389},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a13/}
}
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Moritz Groth. Revisiting the canonicity of canonical triangulations. Theory and applications of categories, Tome 33 (2018), pp. 350-389. http://geodesic.mathdoc.fr/item/TAC_2018_33_a13/