Homotopy Type Theory Univalent Foundations Of Mathematics
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Homotopy Type Theory Univalent Foundations Of Mathematics
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Author :
language : en
Publisher: Univalent Foundations
Release Date :
Homotopy Type Theory Univalent Foundations Of Mathematics written by and has been published by Univalent Foundations this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Homotopy Type Theory
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Author :
language : en
Publisher:
Release Date : 2013
Homotopy Type Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Homotopy theory categories.
The present work has its origins in our collective attempts to develop a new style of "informal type theory" that can be read and understood by a human being, as a complement to a formal proof that can be checked by a machine. Univalent foundations is closely tied to the idea of a foundation of mathematics that can be implemented in a computer proof assistant."--Page vi
Homotopy Type Theory
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Author : Univalent Foundations Program
language : en
Publisher:
Release Date : 2013
Homotopy Type Theory written by Univalent Foundations Program and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Homotopy theory categories.
This book is the product of a yearlong collaboration at the Institute for Advanced Study. It describes (the beta version of) a new language for mathematics, which may some day replace set theory.
Homotopy Type Theory
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Author : Institute for Advanced Study (Princeton, N.J.). School of Mathematics. Univalent Foundations Program
language : en
Publisher:
Release Date : 2013
Homotopy Type Theory written by Institute for Advanced Study (Princeton, N.J.). School of Mathematics. Univalent Foundations Program and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Logic, Symbolic and mathematical categories.
Reflections On The Foundations Of Mathematics
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Reflections On The Foundations Of Mathematics written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
Extended Abstracts Fall 2013
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Author : Maria del Mar González
language : en
Publisher: Birkhäuser
Release Date : 2015-11-12
Extended Abstracts Fall 2013 written by Maria del Mar González and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-12 with Mathematics categories.
The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Geometric Analysis" (thirteen abstracts) and at the "Conference on Type Theory, Homotopy Theory and Univalent Foundations" (seven abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from July 1st to 5th, 2013, and from September 23th to 27th, 2013, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere. The first part is about Geometric Analysis and Conformal Geometry; this modern field lies at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical world, since many natural phenomena posses an intrinsic geometric content. The second part is about Type Theory, Homotopy Theory and Univalent Foundations. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.
Modal Homotopy Type Theory
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Author : David Corfield
language : en
Publisher: Oxford University Press
Release Date : 2020-02-06
Modal Homotopy Type Theory written by David Corfield and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-06 with Philosophy categories.
"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.
Type Theory And Formal Proof
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Author : Rob Nederpelt
language : en
Publisher: Cambridge University Press
Release Date : 2014-11-06
Type Theory And Formal Proof written by Rob Nederpelt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Computers categories.
A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Categories For Types
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Author : Roy L. Crole
language : en
Publisher: Cambridge University Press
Release Date : 1993
Categories For Types written by Roy L. Crole and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.
This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
Category Theory
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Author : Steve Awodey
language : en
Publisher: Oxford University Press
Release Date : 2010-06-17
Category Theory written by Steve Awodey and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-17 with Mathematics categories.
A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.