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Author : F.W. Lawvere
Publisher : Springer
Page : 352 pages
File Size : 25,16 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540374957
A Collection of Lectures by Variuos Authors
Author : M. Makkai
Publisher : Springer
Page : 317 pages
File Size : 24,32 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540371001
Author : P.T. Johnstone
Publisher : Courier Corporation
Page : 401 pages
File Size : 47,46 MB
Release : 2014-01-15
Category : Mathematics
ISBN : 0486493369
Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.
Author : Jacob Lurie
Publisher : Princeton University Press
Page : 944 pages
File Size : 29,30 MB
Release : 2009-07-26
Category : Mathematics
ISBN : 0691140480
In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Author : John L. Bell
Publisher : Courier Corporation
Page : 290 pages
File Size : 48,24 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 0486462862
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Author : Cyrus F. Nourani
Publisher : CRC Press
Page : 296 pages
File Size : 44,36 MB
Release : 2016-04-19
Category : Mathematics
ISBN : 1482231506
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Author : F. W. Lawvere
Publisher :
Page : 354 pages
File Size : 37,54 MB
Release : 1975
Category : Model theory
ISBN :
Author : P. T. Johnstone
Publisher : Oxford University Press
Page : 836 pages
File Size : 23,34 MB
Release : 2002-09-12
Category : Computers
ISBN : 9780198515982
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.
Author : R. Goldblatt
Publisher : Elsevier
Page : 569 pages
File Size : 31,14 MB
Release : 2014-06-28
Category : Mathematics
ISBN : 148329921X
The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.
Author : Patrick Schultz
Publisher : Springer
Page : 235 pages
File Size : 39,74 MB
Release : 2019-01-29
Category : Mathematics
ISBN : 3030007049
This innovative monograph explores a new mathematical formalism in higher-order temporal logic for proving properties about the behavior of systems. Developed by the authors, the goal of this novel approach is to explain what occurs when multiple, distinct system components interact by using a category-theoretic description of behavior types based on sheaves. The authors demonstrate how to analyze the behaviors of elements in continuous and discrete dynamical systems so that each can be translated and compared to one another. Their temporal logic is also flexible enough that it can serve as a framework for other logics that work with similar models. The book begins with a discussion of behavior types, interval domains, and translation invariance, which serves as the groundwork for temporal type theory. From there, the authors lay out the logical preliminaries they need for their temporal modalities and explain the soundness of those logical semantics. These results are then applied to hybrid dynamical systems, differential equations, and labeled transition systems. A case study involving aircraft separation within the National Airspace System is provided to illustrate temporal type theory in action. Researchers in computer science, logic, and mathematics interested in topos-theoretic and category-theory-friendly approaches to system behavior will find this monograph to be an important resource. It can also serve as a supplemental text for a specialized graduate topics course.