Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces

الأصل · EN

In the preceding paper, we have constructed a compactly generated model structure on the category of diffeological spaces together with the adjoint pairs ||:: S and ·: ⁰: R, where and ⁰ denote the category of simplicial sets and that of arc-generated spaces, respectively. In this paper, we show that (||, S) and (·, R) are pairs of Quillen equivalences. Since our approach developed in the preceding paper applies to the category h of Chen spaces as well, h is also a compactly generated model category. We also show that the adjoint pair Sₒ: h: Ch introduced by Stacey is a pair of Quillen equivalences.