, Volume 8, Issue 1, pp 67-116

Universal bivariant algebraic K-theories

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Abstract

To any admissible category of algebras and a family of fibrations on it a universal bivariant excisive homotopy invariant algebraic K-theory is associated. Also, Morita invariant and stable universal bivariant K-theories are studied. We introduce an additive category of correspondencies for non-unital algebras and study the problem of when stable bivariant K-groups can be computed by means of correspondences.

Communicated by Nikolai Vavilov.