Cohomology of categories

General Introduction
This is the same as BauesWirsching cohomology
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Online References
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Paper References
Baues: Homotopy types (e), section 5.
See Generalov in Handbook of Algebra vol 1, in Various folder under ALGEBRA
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
arXiv:1002.1650 The bordism version of the hprinciple from arXiv Front: math.CT by Rustam Sadykov In view of the Segal construction each category with operation gives rise to a cohomology theory. We show that similarly each open stable differential relation R determines cohomology theories k^* of solutions and h^* of stable formal solutions of R. We prove that k^* and h^* are equivalent under a mild condition.
For example, in the case of the covering differential relation our theorem is equivalent to the BarrattPriddyQuillen theorem asserting that the direct limit of classifying spaces B\Sigman of permutation groups \Sigman of finite sets of n elements is homology equivalent to each path component of the infinite loop space \Omega^{\infty}S^{\infty}.
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