# Blog Archives

# Topic Archive: category theory

# Categories turned models: taming the finite

Whereas a category theorist sees mathematics as objects interacting with each other via maps, a model theorist looks instead at their internal structure. So we may think of the former as the sociologues of mathematics and the latter as their psychologues. It is well-known that to a first-order theory we can associate the category of its models, but this produces often a non-natural category, as the maps need to be elementary, and maps rarely are! I will discuss the opposite (Jungian?) perspective: viewing a category as a first-order structure. This yields some unexpected rewards: it allows us to define certain second-order concepts, like finiteness, in a first-order way. I will illustrate this with some examples: sets, modules, topologies, …

# Welcome to the Homotopy Type Theory Reading Group

The goal of this group is to study this:

http://homotopytypetheory.org/book/

Homotopy type theory is a new foundation for mathematics based upon type theory and the univalence axiom. This is a topic that unifies the foundations of mathematics, computer science, algebraic topology, and type theory.

Our first meeting will be on Thursday, September 12th at the CUNY Graduate Center, 365 Fifth Ave, NYC. The time will be 7pm and the room is 8405.

The first talk will be given by Dustin Mulcahey, and will consist of an informal overview of the work. We can also take this time to discuss how we should organize the seminar and split up the talks.

We will be meeting (roughly) every two weeks.

Jointly organized by:

HoTT Reading Group The goal of this group is to study this: http://homotopytypetheory.org/book/ Homotopy type theory is a new foundation for mathematics based upon type theory and the univalence axiom. This is a topic that unifies the foundations of ma …