Free Cocompletions in Category Theory - A Friendly Approach

Explore a Berkeley seminar lecture that delves into the mathematical concept of free cocompletions, focusing on making complex categorical computations more approachable and intuitive. Learn how presheaf categories, while important for free cocompletions under all colimits, can be challenging for calculating colimits compared to simpler polynomial computations. Discover an elementary category structure for small diagrams that models free cocompletion with favorable properties - knowledge previously known to mathematicians like Andrée Ehresmann and Grothendieck. Gain insights into potential applications for generalizing Poly beyond sets of positions and expressing data migrations through functors from categories into free cocompletions. Master concepts related to Poly computations, category theory, and the relationship between Set^op and families in categorical mathematics during this 59-minute advanced mathematical discussion.