Directions for the Long Exact Cohomology Sequence in Moore Categories |
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Authors: | Diana Rodelo |
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Institution: | (1) Universidade do Algarve, Faro, Portugal |
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Abstract: | A new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category
was introduced by Bourn (Cahiers Topologie Géom Différentielle Catég XL:297–316, 1999; J Pure Appl Algebra 168:133–146, 2002). The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore categories we show that they represent a
good context for non-abelian cohomology, in particular for the Baer Extension Theory.
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Keywords: | Realizations of cohomology groups n-Groupoids Barr-exact categories Semi-abelian categories Moore categories |
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