Is there any book of Linear algebra in the modern language of Category theory?
I refer to the (systematic, formalist) study of the category whose objects are vector spaces and whose morphisms are linear maps and its consequences.
Is there any book of Linear algebra in the modern language of Category theory?
I refer to the (systematic, formalist) study of the category whose objects are vector spaces and whose morphisms are linear maps and its consequences.
Filip Bár's master thesis, "On the Foundations of Geometric Algebra" might be a beginning (I don't know if this is online, but perhaps you can ask the author). This thesis develops some ideas by Grassmann in modern language, especially concerning affine spaces and affine algebras, but Chapter 2 deals with vector spaces from a basic categorical point of view.
Meanwhile there are some accounts on commutative algebra from a category-theoretic point of view (Toën-Vezzosi, Lurie, B.).