Abstract:
For many central gadgets in algebraic topology and homotopy theory, allowing ourselves to extend them to new contexts often prove fruitful. This talk aims at motivating why we care about algebraic K-theory, and give some ideas of how (and why) we want to extend the notion of algebraic K-theory from all the way from rings to stable ∞-categories. This will be the first of two talks where we study 1) algebraic K-theory and ∞-categories, and 2) how K-theory and other so-called localizing invariants behave with respect to pullbacks and pushouts.