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Cohomology for Generalized Bredon Coefficient Systems and Higher K-Theory
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- Journal:
- Journal of K-Theory / Volume 12 / Issue 1 / August 2013
- Published online by Cambridge University Press:
- 19 April 2012, pp. 99-113
- Print publication:
- August 2013
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- Article
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Let
be a generalized based category (see definition 1.2). In this paper, we construct a cohomology theory in the category 
of contravariant functors: 
where R is a commutative ring with identity, which generalizes Bredon cohomology involving finite, profinite or discrete groups.We also study higher K-theory of the category
of finitely generated projective objects in and the category 
of finitely generated objects in and obtain some finiteness and other results.
be a generalized based category (see definition 1.2). In this paper, we construct a cohomology theory in the category 
of contravariant functors: 
where 
of finitely generated projective objects in 
of finitely generated objects in 