Explore a mathematical seminar talk that delves into extending algebraic K-theory and other localizing invariants to dualizable stable categories. Learn about the fundamental concepts of dualizable categories and discover how continuous algebraic K-theory functions within these mathematical structures. Understand the relationship between compactly generated categories and their K-theory equivalence to compact object subcategories. Examine the computation methods for continuous K-theory in categories of sheaves on locally compact Hausdorff spaces, and gain insights into an alternative proof of the Kasprowski-Winges theorem regarding K-theory's commutation with infinite products.