Algebraic K‐theory of stable ∞‐categories via binary complexes

Algebraic K-theory via binary complexes

In [11], Quillen defines the notion of exact category. Each such category N is an additive category together with a suitable collection of sequences called short exact sequences. Quillen constructs a space by gluing simplices to each other, using the exact sequences of N to determine the simplices and the gluing instructions. Then for each n ∈ N he defines KnN as a homotopy group of the space. ...

Chain Complexes and Stable Categories

Under suitable assumptions, we extend the inclusion of an additive subcategory X ⊂ A ( = stable category of an exact category with enough injectives) to an S-functor [15] H0]X → A , where H0]X is the homotopy category of chain complexes concentrated in positive degrees. We thereby obtain a new proof for the key result of J. Rickard’s ’Morita theory for Derived categories‘ [17] and a sharpening ...

Derived Algebraic Geometry I: Stable ∞-Categories

Derived Algebraic Geometry I: Stable ∞-Categories

Derived Algebraic Geometry I: Stable ∞-Categories