Michael A. Warren

Carnegie Mellon University
Doctoral student in Pure and Applied Logic


E-mail (remove parentheses and follow the instructions):
m(insert-surname-here)@andrew.cmu.edu

Research Interests

• Category theory
• Mathematical logic and constructive mathematics
• Homotopical algebra

Publications

• Homotopy theoretic models of identity types, with Steve Awodey, Mathematical Proceedings of the Cambridge Philosophical Society, accepted for publication, forthcoming.
  Preprint on the arXiv as arXiv:0709.0248 (math.LO).
  [PS] [PDF] [arXiv]
• Coalgebras in a category of classes, Annals of Pure and Applied Logic, 146(1), pp. 60-71, 2007 (the file here is an early draft and is different from the published paper).
  [PS]
• Predicative algebraic set theory, with Steve Awodey, Theory and Applications of Categories, volume 15, pp. 1-39, 2005.

Preprints and Notes

• A general construction of internal sheaves in algebraic set theory, with Steve Awodey, Nicola Gambino and Peter L. Lumsdaine, 2007 (submitted).
  On the arXiv as arXiv:0711.1529 (math.LO).
  [PS] [PDF] [arXiv]
• Homotopy models of intensional type theory, Ph.D. thesis prospectus, 2006. Available by request.
  Abstract: [PS] [PDF]
• Algebraic models of sets and classes in categories of ideals with Steve Awodey and Henrik Forssell, 2006.
  [PS]
• Predicative categories of classes, M.Sc. thesis in logic, supervisor: Steve Awodey, 2004.
  [PS]
• Gluing categories of classes: disjunction and existence properties for BIST, 2004. Available by request.

Talks Given

• Higher-dimensional groupoids and types, Workshop on Categorical and Homotopical Structures in Proof Theory, Centre de Recerca Matemàtica (Barcelona), February 16 - 17, 2008.
• Model categories and intensional identity types, Workshop on Identity Types - Topological and Categorical Structure (Uppsala), November 13 - 14, 2006.
• Homotopy models of intensional type theory, Foundational Methods in Computer Science (FMCS) 2006 (Kananaskis Field Station, Alberta).
• Coalgebras in a category of classes, Category Theory session of the 2006 Summer meeting of the Canadian Mathematical Society (Calgary).
• Coalgebras in a category of classes, contributed talk at the 2006 annual ASL meeting (Montreal).
• Algebraic set theory: predicativity, Category Theory OctoberFest 2004 (Montreal).
• Logical aspects of the ideal completion of a heyting category, contributed talk at the International Category Theory Conference 2004 (Vancouver).
• Predicative categories of classes, contributed talk at the 2004 annual meeting of the Association for Symbolic Logic (Pittsburgh).

Brief Curriculum Vitae

• Carnegie Mellon University: Doctoral student in Pure and Applied Logic (in progress).
• Carnegie Mellon University: Master of Science in Mathematical Sciences.
• Carnegie Mellon University: Master of Science in Logic and Computation.
• University of St. Andrews: Master of Arts (Honours) First Class in Philosophy.