Obstruction theory in algebraic categories, I

Obstruction Theory in Model Categories

Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obst...

Simulating Algebraic Geometry with Algebra, I: The Algebraic Theory of Derived Categories

This article is the first of three in a series describing recent work by CPS (Ed Cline, Brian Parshall, and myself). I will be concerned here primarily with describing the context of our work and our results on the algebraic theory of derived categories [CPSl]. I will also mention some interesting finite-dimensional algebras of finite global dimension which have arisen in our work. Indeed this ...

Derived Algebraic Geometry I: Stable ∞-Categories

Derived Algebraic Geometry I: Stable ∞-Categories

Derived Algebraic Geometry I: Stable ∞-Categories