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Steve Awodey
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11	Structuralism, Invariance, and Univalence∗ Steve Awodey March 4, 2014 Abstract The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2014-06-01 15:27:23 Homotopy theory Morphisms Category theory Algebraic structures Adjoint functors Isomorphism Groupoid Equivalence of categories Equality Abstract algebra Mathematics Algebra
12	Recent Work in Homotopy Type Theory Steve Awodey Carnegie Mellon University AMS Baltimore January 2014 Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2014-06-01 15:27:30 Abstract algebra Homotopy type theory Groupoid Homotopy Lambda calculus Path Fundamental group Function Hurewicz theorem Homotopy theory Topology Mathematics
13	TOPOLOGY AND MODALITY: THE TOPOLOGICAL INTERPRETATION OF FIRST-ORDER MODAL LOGIC STEVE AWODEY AND KOHEI KISHIDA Abstra t. As M Kinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to al Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2014-06-01 15:27:23 Modal logic Non-classical logic Interpretation Logic Philosophical logic Model theory
14	Voevodsky’s Univalence Axiom in homotopy type theory ´ Steve Awodey, Alvaro Pelayo and Michael A. Warren Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2014-06-01 15:27:23 Abstract algebra Homotopy type theory Homotopy group Homotopy Model category Vladimir Voevodsky Mathematical logic Type theory Out Homotopy theory Topology Mathematics
15	INTRODUCTION TO THE UNIVALENT FOUNDATIONS OF MATHEMATICS CONSTRUCTIVE TYPE THEORY AND HOMOTOPY STEVE AWODEY CARNEGIE MELLON UNIVERSITY Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2014-06-01 15:27:30 Mathematics Groupoid Homotopy type theory Homotopy Model category Fundamental group CW complex Category theory Homotopy theory Topology Abstract algebra
16	Homotopy Type Theory and Univalent Foundations of Mathematics Steve Awodey Carnegie Mellon University Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2014-06-01 15:27:30 Homotopy type theory Homotopy Mathematical logic Algebraic topology Homotopy group Homotopy theory Topology Mathematics
17	Voevodsky’s Univalence Axiom in Homotopy Type Theory Steve Awodey, Álvaro Pelayo, and Michael A. Warren T Add to Reading List Source URL: www.ams.org Language: English - Date: 2013-09-09 12:55:06 Homotopy type theory Homotopy group Homotopy Model category Vladimir Voevodsky Mathematical logic Type theory Algebraic topology Homotopy category Homotopy theory Topology Mathematics
18	Relating first-order set theories, toposes and categories of classes Steve Awodey Add to Reading List Source URL: homepages.inf.ed.ac.uk Language: English - Date: 2013-04-30 07:46:02 Model theory Predicate logic Z notation Sheaf theory Topos Categorical logic Axiom schema of replacement Sheaf Constructive set theory Mathematical logic Mathematics Logic
19	A brief introduction to algebraic set theory∗ Steve Awodey Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2013-10-13 15:36:04 Algebraic structures Boolean algebra Category theory Forcing Heyting algebra Functor Complete Boolean algebra Adjoint functors Topos Mathematics Abstract algebra Algebra
20	TYPE THEORY AND HOMOTOPY STEVE AWODEY Add to Reading List Source URL: www.andrew.cmu.edu Language: English - Date: 2013-10-13 15:36:04 Mathematics Model category Groupoid Homotopy Weak equivalence Fundamental group Simplicial set Fibration Algebraic topology Homotopy theory Topology Abstract algebra

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