Frobenius and Verschiebung for K-theory of Endomorphisms, joint with Sanjana Agarwal, Jonathan Campbell, Kate Ponto, Zhonghui Sun. Submitted.
Coherence for Pseudo Commutative 2-Monads. Submitted.
Coherence for Pseudo Symmetric Multifunctors. In Theory and Applications of Categories. Vol. 41, No. 47, 2024.
Theses:
PhD Thesis: Pseudo symmetric multifunctors: Coherence and Examples. (2024) We prove a coherence theorem for pseudo symmetric multifunctors enriched in Cat as defined by Donald Yau, and provide new examples in the form of a coherence theorem for symmetric pseudo commutative monads. As a consequence we prove that inverse K-theory preserves certain En algebras. In particular, any En-algebra in spectra (parameterized by a free En-operad) can be realized as the K-theory of some permutative category.
Master Thesis: Sheaves of First Order Structures on a Locale. We prove that the category of first order structures on a locale is isomorphic to a certain category of first order structures taking truth values in the locale. This allows us to write down a sheafification functor based on previous work by Fourman and Scott. We also generalize the results obtained by Caicedo for sheaves of structures on a topological space to the locale context.
Undergrad Thesis (in spanish): Chaitin's Ω-Numbers and Incompleteness. We correct the proof of the main theorem in an article by C.S. Calude which generalizes work by Solovay.