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In differential geometry it is often natural to speak of infinite-dimensional manifolds (e.g., the manifold of mappings between two smooth manifolds). Different versions of generalized smooth spaces are proposed for this purpose. I find the most natural and preferable approach: categories of sheaves on suitable sites (among other things, the category is automatically a Grothendieck topos with all the properties that follow). Ideally, I'm looking for a textbook on differential geometry from scratch that actively uses, wherever appropriate, generalized smooth spaces, which are defined as the category of sheaves on some site (this is my only requirement). If such textbooks do not exist, then any literature on generalized smooth spaces of this kind, where some definitions are given and some theorems are proved, would be useful to me.

In differential geometry it is often natural to speak of infinite-dimensional manifolds (e.g., the manifold of mappings between two smooth manifolds). Different versions of generalized smooth spaces are proposed for this purpose. I find the most natural and preferable approach: categories of sheaves on suitable sites (among other things, such categories are automatically Grothendieck topoi with all the properties that follow). Ideally, I'm looking for a textbook on differential geometry from scratch that actively uses, wherever appropriate, generalized smooth spaces, which are defined as the category of sheaves on some site (this is my only requirement). If such textbooks do not exist, then any literature on generalized smooth spaces of this kind, where some definitions are given and some theorems are proved, would be useful to me.

In differential geometry it is often natural to speak of infinite-dimensional manifolds (e.g., the manifold of mappings between two smooth manifolds). Different versions of generalized smooth spaces are proposed for this purpose. I find the most natural and preferable approach: categories of sheaves on suitable sites (among other things, the category is automatically a Grothendieck topos with all the properties that follow). Ideally, I'm looking for a textbook on differential geometry from scratch that actively uses, wherever appropriate, generalized smooth spaces, which are defined as a category of sheaves on some site (this is my only requirement). If such textbooks do not exist, then any literature on generalized smooth spaces of this kind, where some definitions are given and some theorems are proved, would be useful to me.

In differential geometry it is often natural to speak of infinite-dimensional manifolds (e.g., the manifold of mappings between two smooth manifolds). Different versions of generalized smooth spaces are proposed for this purpose. I find the most natural and preferable approach: categories of sheaves on suitable sites (among other things, the category is automatically a Grothendieck topos with all the properties that follow). Ideally, I'm looking for a textbook on differential geometry from scratch that actively uses, wherever appropriate, generalized smooth spaces, which are defined as the category of sheaves on some site (this is my only requirement). If such textbooks do not exist, then any literature on generalized smooth spaces of this kind, where some definitions are given and some theorems are proved, would be useful to me.

In differential geometry it is often natural to speak of infinite-dimensional manifolds (e.g., the manifold of mappings between two smooth manifolds). Different versions of generalized smooth spaces are proposed for this purpose. I find the most natural and preferable approach: categories of sheaves on suitable sites (among other things, the category is automatically a Grothendieck topos with all the properties that follow). Ideally, I'm looking for a textbook on differential geometry that actively uses, wherever appropriate, generalized smooth spaces, which are defined as a category of sheaves on some site (this is my only requirement). If such textbooks do not exist, then any literature on generalized smooth spaces of this kind, where some definitions are given and some theorems are proved, would be useful to me.

In differential geometry it is often natural to speak of infinite-dimensional manifolds (e.g., the manifold of mappings between two smooth manifolds). Different versions of generalized smooth spaces are proposed for this purpose. I find the most natural and preferable approach: categories of sheaves on suitable sites (among other things, the category is automatically a Grothendieck topos with all the properties that follow). Ideally, I'm looking for a textbook on differential geometry from scratch that actively uses, wherever appropriate, generalized smooth spaces, which are defined as a category of sheaves on some site (this is my only requirement). If such textbooks do not exist, then any literature on generalized smooth spaces of this kind, where some definitions are given and some theorems are proved, would be useful to me.