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

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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/