Bordg, Anthony (2018) Univalent Foundations and the UniMath Library. The Architecture of Mathematics. [Preprint]
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Abstract
We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a largescale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander.
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Item Type:  Preprint  

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Additional Information:  To appear in the Synthese Library series, Springer, volume "Reflections on the Foundations of Mathematics: Set Theory, Univalent Foundations and General Thoughts", Chapter II "What are Homotopy Type Theory and the Univalent Foundations?".  
Keywords:  Univalent Foundations, Univalence Axiom, Homotopy Type Theory, UniMath, architecture, formalization of mathematics, proof assistant.  
Subjects:  Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Computer Science General Issues > Structure of Theories 

Depositing User:  Please delete this account  
Date Deposited:  24 Sep 2018 16:32  
Last Modified:  24 Sep 2018 16:32  
Item ID:  15052  
Subjects:  Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Computer Science General Issues > Structure of Theories 

Date:  2018  
URI:  http://philsciarchive.pitt.edu/id/eprint/15052 
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Univalent Foundations and the UniMath Library. (deposited 19 Sep 2018 17:49)

Univalent Foundations and the UniMath Library. The Architecture of Mathematics. (deposited 24 Sep 2018 16:32)
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Univalent Foundations and the UniMath Library. The Architecture of Mathematics. (deposited 24 Sep 2018 16:32)
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