A recipe for black box functors (with Brendan Fong)
Reviewing a principled method for constructing hypergraph categories and functors, known as decorated corelations, in this paper we construct a category of decorating data, and show that the decorated corelations method is itself functorial, with a universal property characterised by a left Kan extension. We then argue that the category of decorating data is a good setting in which to construct any hypergraph functor, giving a new construction of Baez and Pollard's black box functor for reaction networks as an example.
An introduction to locally finitely presentable categories
Notes of my attempt to understand the concept. Contains an introduction, examples, and different characterizations.
Loop spaces and Operads (written in preparation for my A-Exam)
This document serves as an introduction to operads and their algebras, along with basic examples. We review the theory necessary to show May’s recognition principle for loop spaces, and then, following Berger and Moerdijk, present a model structure on the category of operads which allows us to show that every loop space can be rectified to a topological monoid.
Detecting algebraic categories with an internal Hom
Notes for my (chalkboard) presentation at the International Category Theory Conference 2017 as part of the Kan Extension Seminar II.
Category theory in action
Notes for my (whiteboard) presentation at the 43rd Annual New York Regional Graduate Mathematics Conference, a general audience expository talk showing a case where category theory brings something new to the table.
Applying category theory to real life (for real)
Slides for my talk at Cornell's Olivetti Club, about how we can use category theory to model chemical reaction networks.
Infinity-cosmoi and their homotopy 2-categories
Notes for my presentation at the 2018 MIT Talbot Workshop: Model intependent theory of infinity-categories.
Algebra valued functors in general and tensor products in particular
A guest post on the n-Category Cafe, written as part of my participation in the Kan Extension Seminar II.
Dynamical systems and their steady states
A guest post on the n-Category Cafe, written as part of my participation in the Applied Category Theory School.
Infinity and Paradoxes
Problem sets + teaching notes written for the session I led of Cornell's Math Explorer's Club -- a two day, fun activity that introduces new math concepts to high school students.
On the cardinalities of the Fatou and Julia sets
Short final project for a Complex Analysis course.
Simetrias de tres dimensiones homologicas (in Spanish)
Dissertation for my Bachelor in Mathematics (done in Uruguay); abstract in English.