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- W3100814223 abstract "We introduce the groupoidal analogue $widetilde{Theta}$ to Joyal’s cell category Θ and we prove that $widetilde{Theta}$ is a strict test category in the sense of Grothendieck. This implies that presheaves on $widetilde{Theta}$ model homotopy types in a canonical way. We also prove that the canonical functor from Θ to $widetilde{Theta}$ is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on $widetilde{Theta}$ to weak equivalences of presheaves on Θ. Our proofs apply to other categories analogous to Θ." @default.
- W3100814223 created "2020-11-23" @default.
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- W3100814223 date "2011-07-15" @default.
- W3100814223 modified "2023-10-05" @default.
- W3100814223 title "The Groupoidal Analogue $widetilde{{Theta}}$ to Joyal’s Category Θ is a Test Category" @default.
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- W3100814223 doi "https://doi.org/10.1007/s10485-011-9255-2" @default.
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