Axiomatic method and category theory [electronic resource] / Andrei Rodin.
Rodin, Andrei, author.
2014
QA248
Available Online

Linked e-resources

Linked Resource Online Access
Concurrent users Unlimited
Authorized users Authorized users
Document Delivery Supplied Can lend chapters, not whole ebooks

Details

Title Axiomatic method and category theory [electronic resource] / Andrei Rodin.
Author Rodin, Andrei, author.
ISBN 9783319004044 electronic book
3319004042 electronic book
9783319004037
3319004034
9783319004037
DOI https://doi.org/10.1007/978-3-319-00404-4
Published Cham : Springer, 2014.
Language English
Description 1 online resource (xi, 285 pages) : illustrations.
Item Number 10.1007/978-3-319-00404-4 doi
Call Number QA248
Dewey Decimal Classification 511.3/22
Summary This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on online resource; title from PDF title page (SpringerLink, viewed October 21, 2013).
Series Synthese library ; v.364.
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
A Brief History of the Axiomatic Method
Identity and Categorification
Subjective Intuitions and Objective Structures.

Browse Subjects

Show more subjects...

Statistics

from
to
Export