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Abstract: In previous work, we showed that there are appropriate model categorystructures on the category of simplicial categories and on the category ofSegal precategories, and that they are Quillen equivalent to one another and toRezk-s complete Segal space model structure on the category of simplicialspaces. Here, we show that these results still hold if we instead use groupoidor -invertible- cases. Namely, we show that model structures on the categoriesof simplicial groupoids, Segal pregroupoids, and invertible simplicial spacesare all Quillen equivalent to one another and to the standard model structureon the category of spaces. We prove this result using two different approachesto invertible complete Segal spaces and Segal groupoids.



Author: Julia E. Bergner

Source: https://arxiv.org/







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