The existence of a model structure on the category \({\mathcal {D}}\) of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model structure on the category \({\mathcal {D}}\) whose weak equivalences are just smooth maps inducing isomorphisms on smooth homotopy groups. The essential part of our construction of the model structure on \({\mathcal {D}}\) is to introduce diffeologies on the sets \(\varDelta ^{p}\)\((p \ge 0)\) such that \(\varDelta ^{p}\) contains the \(k\mathrm{th}\) horn \(\varLambda ^{p}_{k}\) as a smooth deformation retract.

中文翻译：

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不同空间的模型类别

在差分空间\（{\ mathcal {D}} \）上模型结构的存在对于发展光滑同伦论至关重要。我们在类别\（{\ mathcal {D}} \）上构造一个紧凑生成的模型结构，其弱等价性只是在光滑同伦群上诱导同构的光滑图。我们的模型上的结构的结构的主要部分\（{\ mathcal {d}} \）是上套引入diffeologies \（\ varDelta ^ {P} \）\（（对\ GE 0）\）这样即\（\ varDelta ^ {p} \）包含\（K \ mathrm {第} \）喇叭\（\ varLambda ^ {p} _ {K} \）为平滑变形回缩。