Nationality American Name Michael Shulman | Role Mathematician Doctoral advisor J. Peter May | |

Fields Category theory
Homological algebra
Homotopy type theory Institutions University of San Diego Institute for Advanced Study Alma mater California Institute of Technology Institution University of San Diego, Institute for Advanced Study |

## Inernal languages for higher toposes michael shulman

**Michael** "**Mike**" **Shulman** (; born 1980) is an American mathematician at the University of San Diego who works in category theory and higher category theory, homotopy theory, logic as applied to set theory, and computer science. He did his undergraduate work at the California Institute of Technology and his postgraduate work at the University of Cambridge and the University of Chicago, where he received his Ph.D. in 2009.

## Contents

- Inernal languages for higher toposes michael shulman
- Gluing in homotopy type theory michael shulman
- Work
- Blogs
- Selected publications
- References

## Gluing in homotopy type theory michael shulman

## Work

Shulman's doctoral thesis and subsequent work dealt with applications of category theory to homotopy theory. In 2009, he received a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship.

From September 2012 to April 2013, he was a visiting scholar at the Institute for Advanced Study, where he was one of the official participants in the *Special Year on Univalent Foundations of Mathematics*. Along with fellow researchers, such as Andrej Bauer and Steve Awodey, Shulman was one of the principal authors of the book *Homotopy type theory: Univalent foundations of mathematics*, which summarized much of the work of the Special Year and has become a benchmark in the new field of homotopy type theory. In 2014, Shulman was part of a team headed by Steve Awodey that was awarded a $7.5M grant from the Air Force Research Laboratory for homotopy type theory.

## Blogs

Shulman is a supporter of using web-based software systems, such as GitHub, to promote collaborative work by mathematicians — the six-hundred-page HoTT Book being a notable example. He is a prolific contributor to the nLab (and a member of its steering committee), and a co-host of the homotopy type theory blog and of the *n*-Category Cafe, a blog focusing on higher category theory.

## Selected publications

*Synthetic Differential Geometry*May 31, 2006

*Calculating the fundamental group of the circle in homotopy type theory*January 15. 2013

*Univalent categories and the Rezk completion*March 4. 2013

*Univalence for inverse diagrams and homotopy canonicity*November 23, 2013

*Lectures on n*In Baez, John C.; May, J. Peter, eds. (2009).

*-categories and cohomology**Towards Higher Categories*. Springer. ISBN 1441915230.