2026-08-14 –, R. 221
Often we define functors F where each object F(A) satisfies a universal property; these could be products, limits, colimits, (co)ends, (co)free objects, kan extensions, exponential objects... Usually, existence and uniqueness of the mediating morphisms allow you to define the functorial action and verify functoriality, respectively. But as these constructions get more complicated, the diagram-chasing gets more and more tedious, and one gets the feeling that there should be some universal theorem giving functoriality for free.
This talk will show such a silver bullet does exist! In these situations of a parametrised family of universal properties there is an economical, "maximally lazy" way to define your functors on objects, and deduce the action on morphisms.
Greetings! My name is Ruby Khondaker. I'm a PhD student in condensed matter physics at the University of Oxford, whose current research is to do with low-energy properties of the eigenstates of SYK, especially at finite N.
I came across category theory during my masters, after an undergrad that had largely disillusioned me with pure maths, and instantly fell in love with the subject. While it's more of a hobby for me at the moment, category theory actually has quite major applications in condensed matter. There are lots of interesting topological, homotopical and categorical phenomena that arise naturally in the study of quantum materials, so I am speedrunning some textbooks to learn about (and hopefully one day contribute) to this!
I run a math blog which is mostly about using the ideas of category theory in a pedagogical sense, to teach math concepts one might meet in early university from a new perspective. Other than that I'm a big anime and gaming nerd, especially anything Toby Fox has made! You'll likely be seeing my Ralsei plush a bunch over the course of the conference :)