nLab Mike Shulman

I am an Associate Professor at the University of San Diego. Here is my web page.

I have recently been deeply involved in homotopy type theory. I am also interested in (higher) category theory and its applications to the rest of mathematics, particularly homotopy theory. I also tend to be a partisan of higher-categorical structures other than $n$-categories (such as double categories, multicategories, proarrow equipments, F-categories, and so on), which sometimes seem to get neglected.

Personal area

For my own reference: some pages that I was once planning to do some work on:

• theory
• lax 2-adjunction
• structured (infinity,1)-topos and classifying topos
• generalized multicategory, virtual double category, virtual equipment
• functoriality of codiscrete cofibrations,
• create a separate page two-sided fibration, also work on fibration in a 2-category
• categories over computads at monadicity theorem.
• copy some stuff over from my personal web
• write descent object

And here’s how to make a barred arrow $A ⇸ B$, since I always forget:

  ⇸

And here’s the esh $ʃ$ (see here):

  ʃ

Selected writings

On modal type theory:

• Mike Shulman, Semantics of multimodal adjoint type theory (arXiv:2303.02572)

On cohesive homotopy type theory:

• Mike Shulman, Brouwer’s fixed-point theorem in real-cohesive homotopy type theory, Mathematical Structures in Computer Science Vol 28 (6) (2018): 856-941 (arXiv:1509.07584, doi:10.1017/S0960129517000147)

• Mike Shulman, Homotopy type theory: the logic of space, New Spaces in Mathematics: Formal and Conceptual Reflections, ed. Gabriel Catren and Mathieu Anel, Cambridge University Press, 2021 (arXiv:1703.03007, doi:10.1017/9781108854429)

Talks

On higher observational type theory:

• Michael Shulman, Towards a Third-Generation HOTT:, talk at Homotopy Type Theory at CMU (2022) [part 1: slides, video; part 2: slides, video; part 3: slides, video]

category: people