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Limits and colimits in synthetic ∞-categories.

Published in Submitted preprint, 2022

We develop a theory of limits and colimits in the setting of synthetic ∞-categories.

Recommended citation: Bardomiano Martínez, César. “Limits and Colimits in Synthetic ∞-Categories.” Mathematical Structures in Computer Science 35 (2025): e24. https://doi.org/10.1017/S0960129525100248. https://doi.org/10.1017/S0960129525100248

Exponentiable functors between synthetic ∞-categories

Published in Submitted preprint, 2024

We study exponentiable functors in simplicial type theory. Submitted

Recommended citation: Bardomiano Martínez, César. “Exponentiable Functors between Synthetic ∞-Categories.” Mathematical Structures in Computer Science 35 (2025): e29. https://doi.org/10.1017/S0960129525100339. https://doi.org/10.1017/S0960129525100339

The language of a model category

Published in Preprint, 2025

We explore a beautiful and intriguing relation between logic and homotopy theory. In this joint work with Simon Henry, we build the notion of a language over a model category. Throughout it, we hope to get some insights about models of infinity categories.

Recommended citation: Arxiv preprint!

Limits and colimits of synthetic (∞,1)-categories.

Published: February 10, 2022

Talk for the Logic Seminar in the Deparment of Mathematics at UOttawa at the University of Ottawa.s

Limits and colimits in simplicial homotopy type theory

Published: September 19, 2023

Contributed talk during the Interactions of Proof Assistants and Mathematics Summer School at Regensburg.

The language of a model category

Published: June 27, 2024

Contributed talk during the Category Theory Conference 2024 (CT2024).

The language of a model category

Published: July 08, 2024

Contributed talk at the Foundational methods in computer science in Kananaskis, AB.

The language of a model category

Published: December 19, 2024

Speed talk at the Categorical logic and higher categories conference

Homotopy languages

Published: January 30, 2025

Invited talk for the ASSUME joint seminar on Univalent foundations between Universities of Birmingham and Notthingham.

National Autonomous University of Mexico (UNAM)

Teaching, Faculty of Sciences, 2016

• Lecturer for the course Linear Algebra I during the 2018 Winter semester.
• Lecturer for the course Superior Algebra I during the 2018 Winter semester for the Faculty of Higher Studies Acatlan.
• I was teaching assistant for a number of courses too (from 2016 to 2018):
  • Linear algebra I.
  • Number theory I.
  • Algebra I.
  • Algebra II.

University of Western Ontario

Teaching assistant, Department of Mathematics and Statistics, 1900

I was teaching assitant for:

• Calculus.
• Methods of matrix algebra.
• Methods of finite mathematics.

University of Ottawa

Teaching assistant, Department of Mathematics and Statistics, 2021

This semester I am a Lecturer for Calculus II (Mat 1322).