Joyal范畴Theta的类群Theta~是一个测试范畴
The groupoidal analogue Theta~ to Joyal's category Theta is a test category
摘要：
我们在Joyal的胞范畴Θ中引入群胚类似物\tilde Θ，并证明了\tilde Θ是Grothendieck意义下的严格检验范畴.这意味着在\tilde Θ模型同伦类型上的预层是典型的。我们还证明了从Θ到\tilde Θ的正则函子是非球面的，也是在Grothendieck意义下。这使得我们可以比较\tilde Θ上的预层的弱等价和Θ上的预层的弱等价。我们的证明适用于类似于Θ的其他范畴。
英文摘要：
We introduce the groupoidal analogue \tildeΘto Joyal's cell category Θand we prove that \tildeΘis a strict test category in the sense of Grothendieck. This implies that presheaves on \tildeΘmodel homotopy types in a canonical way. We also prove that the canonical functor from Θto \tildeΘis aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tildeΘto weak equivalences of presheaves on Θ. Our proofs apply to other categories analogous to Θ.
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