Homotopy in exact categories (Q6605397)

In this book, the author starts with a review of exact categories in the sense of \textit{D. Quillen} [Lect. Notes Math. 341, 85--147 (1973; Zbl 0292.18004)] building on \textit{T. Bühler} [Expo. Math. 28, No. 1, 1--69 (2010; Zbl 1192.18007)]. This includes several homological lemmas, different notions of exactness of complexes and functors, the homotopy and derived category for weakly idempotent complete exact categories and notions like projective objects, monodial exact categories and generators (Chapter 2). In Chapter 3, Kelly discusses, as examples, Banach modules over a Banach ring and the category \(\operatorname{Ind}(\operatorname{Ban}_k)\) of Ind-objects of Banach spaces over a Banach field \(k\); the latter is closely related to the category of bornological spaces, see [\textit{R. Meyer}, Local and analytic cyclic homology. Zürich: European Mathematical Society (EMS) (2007; Zbl 1134.46001)]. In Chapter 4 Kelly discusses model structures on categories of chain complexes over an exact category. A general condition is given under which unbounded complexes are equipped with the projective model structure and it is surveyed when such a model structure is monoidal. In Chapter 5, filtered and graded objects in exact categories are treated. In the final Chapter 6, Kelly investigates under which conditions categories of chain complexes over an exact category form a so-called homotopical algebra context.