University of South Florida

College of Arts and Sciences

Search

Menu

Give Now

Title: An Idiosyncratic Introduction to Category Theory III: Functors Speaker: Greg McColm Time: 2:00pm–3:00pm Place: Zoom Meeting

The homomorphisms and antimorphisms of categories are the functors, and they have a number of applications in category theory. For example, sometimes a global operation on a category is a functor; sometimes a standard map from one category to another is a functor. And many constructions within a category can be defined using a functor from a diagram to that category. Functors can even be used to enable the dissection of objects in one category via objects in another. We take a brief excursion look at functors and ultimately at that very odd creature, the category of categories.

Title: An Idiosyncratic Introduction to Category Theory II: Some basic constructions Speaker: Greg McColm Time: 2:00pm–3:00pm Place: Zoom Meeting

A category consists of objects and morphisms, but since category theory is supposed to be able to handle all known mathematics, there are literally zillions of constructions for handling this or that kind of mathematical subject. We look at a few of these, popular ones like products and coproducts (thus introducing the notion of “duality”), unjustifiably neglected ones like unions and intersections, generalizations like limits and colimits, and perhaps a few others as time permits. We will look at some examples of how to build complicated objects using these constructions.

Title: An Idiosyncratic Introduction to Category Theory I: Categories of the Objects You Meet in Math Classes Speaker: Greg McColm Time: 2:00pm–3:00pm Place: Zoom Meeting

Category Theory is very abstract because it is supposed to be able to handle any kind of mathematical object. Many of the objects we encounter in mathematics classes are complex structures like functions, graphs, groups, probability distributions, topological spaces, and much of category theory involves comparisons of like structures. In this first talk, we look at categories of this kind and a few of the more common constructions.