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- W2767339927 abstract "We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of augmentation categories, which are a special class of generalised Reedy categories. For an augmentation category, we prove the existence of a closed Quillen model structure on the presheaf category which is compatible with the Kan-Quillen model structure on simplicial sets. Moreover, we use the concept of augmented hypercovers to define a local model structure on the category of augmented presheaves. We prove that crossed simplicial groups, and the planar rooted tree category are examples of augmentation categories. Finally, we introduce a method for generating new examples from old via a categorical pushout construction." @default.
- W2767339927 created "2017-11-17" @default.
- W2767339927 creator A5066303010 @default.
- W2767339927 date "2017-11-17" @default.
- W2767339927 modified "2023-09-27" @default.
- W2767339927 title "Augmented Homotopical Algebraic Geometry" @default.
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