A coherence theorem for pseudo symmetric multifunctors, (2023) Submitted.
Multicategories are a setup for working with multi input or multilinear maps even in the absence of tensor products. They are used in the study of multiplicative `K`-theory, with `K`-theory being defined as a multifunctor that preserves multiplicative structures encoded using multicategories. In this article I study multifunctors that preserve the action of the symmetric group on the hom spaces of multicategories by permuting inputs only up to coherent isomorphisms. These were first defined by Donald Yau, who proved that Mandell's inverse `K`-theory multifunctor is pseudosymmetric. As a consequence of the coherence result I prove, pseudo symmetric multifunctors preserve `E_n` algebras. This result also helps easily describe 2-categories whose 0-cells are symmetric multicategories and whose 1-cells are pseudo symmetric multifunctors, like the one defined by Yau.
Master thesis: Logic of sheaves of structures on a locale, (2015).
I generalized Caicedo's Generic Model Theorem for sheaves of first order structures on a topological space to sheaves of first order structures on a locale.
Undergraduate thesis (in spanish): Números Omega de Chaitin, Máquinas de Solovay e Incompletez, (2012).
I filled the gaps in a proof by Calude of a generalization of a theorem by Solovay.