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Homotopy theory with C*-categories

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OASW02 - Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras

 In this talk I propose a presentable infinity category of C-categories. It is modeled by a simplicial combinatorial model category structure on the category of C-categories. This allows to set up a theory of presheaves with values in C*-categories on the orbit category of a group together with various induction and coinduction functors. As an application we provide a simple construction of equivariant K-theory spectra (first constructed by Davis-Lück). We discuss further applications to equivariant coarse homology theories.

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