Department of Mathematics - Master Calendar

Abstract: Category theory provides an essential framework for many areas of mathematics, ranging all the way from algebra to geometry. One of the central philosophies of category theory is encoded in the Yoneda lemma, which heuristically says understanding a mathematical object is the same as understanding maps into it, or maps out of it. This philosophy exists in many extensions of category theory, including enriched category theory, quasi-categories, and n-fold categories. 

One of the fundamental consequences of the Yoneda lemma is that we can consider dependent products over categories, allowing for a powerful internal logic in category theory. In this talk we will discuss the relationship between the existence of such dependent products, the existence of Yoneda lemmas, and the existence of factorizations in certain weak extensions of category theory.