# Homotopy theory with *-categories

## Ulrich Bunke

We construct model category structures on various types of (marked) *-categories. These structures are used to present the infinity categories of (marked) *-categories obtained by inverting (marked) unitary equivalences. We use this presentation to explicitly calculate the $\infty$-categorical G-fixed points and G-orbits for G-equivariant (marked) *-categories.

Keywords: *-categories, model categories, $\infty$-categories, limits and colimits

2010 MSC: 18C35,55U35

Theory and Applications of Categories, Vol. 34, 2019, No. 27, pp 781-853.

Published 2019-09-16.

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