WEBstep in the direction of such a connection between homotopy theory and type theory by providing several new models of type theory using structures and techniques from homotopy theory and higher-dimensional category theory.
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WEBCarnegie Mellon University Homotopy Theoretic Aspects of Constructive Type Theory Michael Alton Warren August 2008 Committee Steven M. Awodey (chair) Nicola …
Homotopy Theoretic Aspects of Constructive Type Theory
WEBCorpus ID: 123575477 Homotopy Theoretic Aspects of Constructive Type Theory @inproceedings{Warren2008HomotopyTA, title={Homotopy Theoretic Aspects of …
Michael A. Warren
WEBHomotopy theoretic models of identity types, with Steve Awodey, Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 45-55, 2009. Preprint …
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Type Theory and Homotopy | SpringerLink
- Groupoids and their homomorphisms arise in homotopy theory as a “model” (i.e. a representation) of topological spaces with homotopy classes of continuous maps. There are other models as well, such as simplicial sets. The idea of a Quillen model category (cf. Quillen 1967; Bousfield 1977) is to axiomatize the common features of these different model...
- Author: Steven Awodey
- Publish Year: 2012
Introduction – from type theory and homotopy theory to ...
WEBWarren, M. A. ( 2008) Homotopy Theoretic Aspects of Constructive Type Theory, Ph.D. thesis, Carnegie Mellon University. Google Scholar. Introduction – from type theory and …
WEBChapter 9. Type Theory and Homotopy. Steve Awodey. 9.1 Introduction. The purpose of this informal survey article is to introduce the reader to a new and surprising connection …
WEBThe new approach presented here constructs a bridge from con-structive type theory to algebraic topology, exploiting both the ax-iomatic approach to homotopy of Quillen …
Constructive Type Theory - The Handbook of Contemporary ...
WEBAug 21, 2015 · Constructive Type Theory. Aarne Ranta. Book Editor (s): Shalom Lappin, Chris Fox. First published: 21 August 2015. …
Homotopy type theory: unified foundations of mathematics ...
WEBJan 28, 2015 · Homotopy type theory is a recently-developed unification of previously disparate frameworks, which can serve to advance the project of formalizing and …
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