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Higher Categories from Type Theories Peter LeFanu Lumsdaine

Summary: Higher Categories from Type Theories
PhD thesis
Peter LeFanu Lumsdaine
Doctoral Dissertation
Department of Mathematics
Carnegie Mellon University
Higher Categories from Type Theories
Peter LeFanu Lumsdaine
20 December, 2010
This thesis continues the programme of providing a higher-categorical anal-
ysis of the treatment of equality in Martin-Lof dependent type theory.
In particular, we construct for various type theories a classifying weak
-category, with objects and 1-cells as in the standard classifying category,
and higher cells being open terms of identity types between these. Weak
-category structures (in the sense of Batanin/Leinster) on these are given
by operads of syntactically definable composition laws.
Steve Awodey (doctoral advisor)
James Cummings (chair)


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics