Nuclear Ideals in Monoidal *-Categories

Explore a mathematical lecture that delves into quantitative analogues of binary relations and nuclear ideals in monoidal *-categories, presented at the Topos Institute Colloquium. Learn about groundbreaking research developed with Samson Abramsky and Richard Blute that introduces nuclear ideals as a generalization of nuclear maps from functional analysis. Discover how compact closed structures associated with relation categories evolve into nuclear ideals, and examine how certain morphisms behave within compact closed categories. Investigate two novel examples of monoidal *-categories where integration serves as composition - one involving tame distributions and another based on measure and probability theory that offers insights into probabilistic relations. Gain understanding of how nuclear morphisms relate to Hilbert-Schmidt maps in the category of Hilbert spaces, and explore concepts associated with trace ideals in modern mathematical developments.