Cult of Categories & Types

Welcome to the captivating world of abstract mathematics! Our seminar group is a haven for those who are intrigued by the intricate interplay of Category Theory, Higher Category Theory, and Homotopy Type Theory.

Category theory provides a unifying framework and a linguistic template for understanding and comparing various mathematical structures and processes. It seeks to capture the essence of mathematical concepts by focusing on the relationships between them, transcending the particulars of individual objects. 

Venturing deeper, we will encounter the enigmatic realm of Higher Category Theory. We will explore n-categories, n-functors, and n-transformations, where the integer n which goes all the way upto ∞, signifies the dimension of these structures. Through captivating discussions and thought-provoking examples, we will unwrap the beauty and complexity of these higher categorical concepts.

Homotopy Type Theory (HoTT), a revolutionary field that combines concepts from Homotopy Theory and Type Theory, brings an exciting new perspective to the seminar. HoTT blurs the boundaries between Logic, Topology, and Computation by introducing a correspondence between types and spaces, suggesting that types can be viewed as topological spaces. This fresh perspective has deep implications for both mathematics and computer science, and we will embark on a journey to understand the nuances and implications of this theory.

If you are interested in learning more about these subjects, or if you are simply curious about how Category Theory can be used to unify mathematics, then please join us for the seminar!