A proposition is the (homotopy) type of its proofs Steve Awodey∗ January 8, 2016 There are, at first blush, two kinds

Source URL: www.andrew.cmu.edu

Univalence as a Principle of Logic Steve Awodey October 2016 Abstract It is sometimes convenient or useful in mathematics to treat isomorphic structures as the same. The recently proposed Univalence Axiom for the foundat

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A cubical model of homotopy type theory∗ Steve Awodey Stockholm, 21 June 2016 The main goal of these notes is to prove the following: Theorem. There is an algebraic weak factorization system (L, R) on the category of c

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Notes on Algebraic Set Theory Steve Awodey Haute-Bodeux, June 2005

Source URL: www.phil.cmu.edu

Algebraic models of sets and classes in categories of ideals Steve Awodey and Henrik Forssell and Michael A. Warren May 31, 2006 Revised: November 2006

Source URL: www.phil.cmu.edu

Homotopy-initial W-types Nicola Gambino University of Palermo Joint work with Steve Awodey and Kristina Sojakova Manchester, Logic Colloquium 2012

Source URL: www.cl.eps.manchester.ac.uk

Propositions as [Types] Steve Awodey∗ Andrej Bauer† Institut Mittag-Leffler

Source URL: andrej.com

• Proof theory
• Deduction
• Algebraic topology
• Curry–Howard correspondence
• Philosophy of computer science
• Type theory
• Entailment
• Sheaf
• Natural deduction
• Logic
• Abstract algebra
• Mathematics

Academic Report / “Sachbericht” ([removed]–[removed]Hannes Leitgeb, April 23rd 2013 The Munich Center for Mathematical Philosophy (MCMP) enjoyed another lovely and exciting year[removed]From October 2012, Stephan

Source URL: www.mcmp.philosophie.uni-muenchen.de

• Mathematics
• Deontic logic
• Formal epistemology
• Steve Awodey
• Norm
• Modal fictionalism
• Linguistic modality
• Formal ethics
• Homotopy type theory
• Logic
• Mathematical logic
• Modal logic

arXiv:1403.0020v1 [math.LO] 28 Feb[removed]Topos Semantics for Higher-Order Modal Logic Steve Awodey∗ Kohei Kishida†

Source URL: www.andrew.cmu.edu

• Sheaf theory
• Heyting algebra
• Lattice theory
• Mathematical constructivism
• Order theory
• Topos
• Adjoint functors
• Sheaf
• Subobject classifier
• Category theory
• Abstract algebra
• Mathematics

Natural models of homotopy type theory Steve Awodey 1 June 2014 Abstract The notion of a natural model of type theory is defined in terms of that

Source URL: www.andrew.cmu.edu

• Mathematics
• Homotopy theory
• Differential topology
• Sheaf
• Functor
• Grothendieck topology
• Section
• Adjoint functors
• Initial and terminal objects
• Topology
• Abstract algebra
• Algebraic topology