Cohomology theory in 2-categories
| dc.creator | Nakaoka, Hiroyuki | |
| dc.date | 2008-11-17 | |
| dc.date.accessioned | 2026-07-07T10:18:47Z | |
| dc.date.available | 2026-07-07T10:18:47Z | |
| dc.description | 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 $\mathrm{SCG}$ are being investigated. In this paper, we consider a 2-categorical analogue of an abelian category, in such a way that it contains $\mathrm{SCG}$ 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. | |
| dc.identifier | https://arxiv.org/abs/0811.2627 | |
| dc.identifier | http://arxiv.org/abs/0811.2627 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174307 | |
| dc.subject | Category Theory | |
| dc.title | Cohomology theory in 2-categories | |
| dc.type | text |