Michael Shulman: Papers

I am interested in category theory and higher category theory and their applications to the rest of mathematics, especially homotopy theory, logic/set theory, and computer science. Here is a list of all my published papers, preprints, notes, and other stuff I've written related to math. Some of it is research and some of it is just expository.

Blogs and wikis

• I am a co-host of The n-Category Cafe, a group blog about math, physics and philosophy, especially as they relate to higher categories.
• I am a contributor to the nLab, a research wiki for collaborative work on the same subjects.

Papers and preprints

Here are all my "official" non-blog, non-wiki writings, in roughly reverse chronological order by date of appearance.

• Unbounded quantifiers and strong axioms in topos theory: Preprint not yet publically available, but you can see the slides for the talk I gave at NovemberFest 2009.
• (with Kate Ponto) Shadows and traces in bicategories; preprint available on the arXiv: 0910.1306. You can also see the slides of a mostly expository talk I gave at CCR La Jolla here.
• (with Geoff Cruttwell) A unified framework for generalized multicategories : preprint available on the arXiv: 0907.2460.
• The internal logic of a 2-topos: An ongoing project; its current status can be seen on my section of the nLab.
• Set theory for category theory: an exposition of various set-theoretical foundations for category theory and their implications. Available on the arXiv: 0810.1279.
• Comparing composites of left and right derived functors: preprint available on the arXiv: 0706.2868. I gave a talk about this at the JMM '09; you can see the slides here.
• Parametrized spaces model locally constant homotopy sheaves. Topology Appl. 155 (2008), no. 5, 412–432. Also available at arXiv:0706.2874.
• Framed bicategories and monoidal fibrations. Theory and Applications of Categories 20 (2008), no. 18, 650–738. Available online here and also on the arXiv:0706.1286.
• (with John Baez) Lectures on n-categories and cohomology. In Towards Higher Categories, IMA Volumes in Mathematics and its Applications, Springer 2009. Based on notes I took on a series of expository talks given by John, plus an appendix. Also available on the arXiv: math.CT/0608420.
• Homotopy limits and colimits and enriched homotopy theory: preprint available on the arXiv: math/0610194.
• Anchored Bicategories: The slides for the talk I gave at the Mac Lane Memorial Conference on April 11, 2006 can be found here. All the material except the last half-dozen slides can now be found, in improved form, in 0706.1286 ("Framed bicategories and monoidal fibrations").

Notes

Some notes from expository talks I've given.

• Generators and colimit closures: notes from a talk in the category theory proseminar at Chicago. [PDF]
• Ultrafilters, Pseudotopological spaces, and Stone-Cech compactification: notes from a talk at the graduate student pizza seminar at Chicago on January 23, 2008. [PDF]
• Synthetic differential geometry: notes from a talk at the graduate student pizza seminar at Chicago on May 31, 2006. [PS] [PDF]