Geodesic
Cohomology theory in 2-categories
Theory and applications of categories, Tome 20 (2008), pp. 543-604

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups SCG are being investigated. In this paper, we consider a 2-categorical analogue of an abelian category, in such a way that it contains SCG as an example. As a main theorem, we construct a long cohomology 2-exact sequence from any extension of complexes in such a 2-category. Our axiomatic and self-dual definition will enable us to simplify the proofs, by analogy with abelian categories.

Classification : 18D05
Keywords: symmetric categorical group, 2-category, cohomology, exact sequence 
@article{TAC_2008_20_a15,
     author = {Hiroyuki Nakaoka},
     title = {Cohomology theory in 2-categories},
     journal = {Theory and applications of categories},
     pages = {543--604},
     publisher = {mathdoc},
     volume = {20},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2008_20_a15/}
}
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Hiroyuki Nakaoka. Cohomology theory in 2-categories. Theory and applications of categories, Tome 20 (2008), pp. 543-604. http://geodesic.mathdoc.fr/item/TAC_2008_20_a15/