Topoi
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Topoi
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Author : R. Goldblatt
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Topoi written by R. Goldblatt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
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.
Transforming Topoi
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Author : Andrew James Johnston
language : en
Publisher: V&R Unipress
Release Date : 2018-09-10
Transforming Topoi written by Andrew James Johnston and has been published by V&R Unipress this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-10 with History categories.
Traditionen leben von der Dialektik der Wiederholung, die das Gleiche stets anders inszeniert. Sie speisen sich aus den Erinnerungen; an der Grenze von bedacht und selbstverständlich getan lassen sie sich nur als selbstverständliche Überzeugungen bestimmen. Aber wie ist es dennoch möglich, Traditionen zu beeinflussen? Der vorliegende Band widmet sich der Frage, wie man mit Traditionen Symbolpolitik machen kann. Was sind die Zumutungen der Traditionen, wenn sie politisch instrumentalisiert werden? Gibt es Grenzen der Manipulation, die im Wesen der jeweiligen Traditionen liegen und sie folglich definieren? Die BeiträgerInnen geben eine Vielzahl von Antworten, indem sie sich Topoi aus Mittelalter und Früher Neuzeit aus interdisziplinärer Perspektive widmen. Traditions thrive on the dialectic of repetition. Drawing their topoi from the well of memory, they are situated on the very border between the deliberate and the habitual. Yet how is it possible to influence traditions? The present collection of essays studies the ways in which traditions are employed in the service of symbolic politics. What are the burdens and impositions of traditions, when their topoi are consciously exploited in the service of ideological purposes? Are there certain limits to manipulation that lie in the very nature of the traditions in question, a nature which therefore defines them? The contributors give a host of answers, studying topoi in medieval and early modern Europe from an interdisciplinary perspective.
Forcing And Classifying Topoi
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Author : Andrej Ščedrov
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Forcing And Classifying Topoi written by Andrej Ščedrov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Categories categories.
We give a general method of forcing over categories as a category-theoretic universal construction which subsumes, on one hand, all known instances of forcing in set theory, Boolean and Heyting valued models and sheaf interpretations for both classical and intuitionistic formal systems; and, on the other hand, constructions of classifying topoi in topos theory.
Lecture Notes On Topoi And Quasitopoi
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Author : Oswald Wyler
language : en
Publisher: World Scientific
Release Date : 1991
Lecture Notes On Topoi And Quasitopoi written by Oswald Wyler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Quasitopoi generalize topoi, a concept of major importance in the theory of Categoreis, and its applications to Logic and Computer Science. In recent years, quasitopoi have become increasingly important in the diverse areas of Mathematics such as General Topology and Fuzzy Set Theory. These Lecture Notes are the first comprehensive introduction to quasitopoi, and they can serve as a first introduction to topoi as well.
Classifying Spaces And Classifying Topoi
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Author : Izak Moerdijk
language : en
Publisher: Springer
Release Date : 2006-11-14
Classifying Spaces And Classifying Topoi written by Izak Moerdijk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces. The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.
Model Theory And Topoi
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Author : F.W. Lawvere
language : en
Publisher: Springer
Release Date : 2006-11-15
Model Theory And Topoi written by F.W. Lawvere and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
A Collection of Lectures by Variuos Authors
Topoi Graphein
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Author : Christian Abrahamsson
language : en
Publisher: U of Nebraska Press
Release Date : 2018-05
Topoi Graphein written by Christian Abrahamsson and has been published by U of Nebraska Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05 with Philosophy categories.
In Topoi/Graphein Christian Abrahamsson maps the paradoxical limit of the in-between to reveal that to be human is to know how to live with the difference between the known and the unknown. Using filmic case studies, including Code Inconnu, Lord of the Flies, and Apocalypse Now, and focusing on key concerns developed in the works of the philosophers Deleuze, Olsson, and Wittgenstein, Abrahamsson starts within the notion of fixed spatiality, in which human thought and action are anchored in the given of identity. He then moves through a social world in which spatiotemporal transformations are neither fixed nor taken for granted. Finally he edges into the pure temporality that lies beyond the maps of fixed points and social relations. Each chapter is organized into two subjects: topoi, or excerpts from the films, and graphein, the author’s interpretation of presented theories to mirror the displacements, transpositions, juxtapositions, fluctuations, and transformations between delimited categories. A landmark work in the study of human geography, Abrahamsson’s book proposes that academic and intellectual attention should focus on the spatialization between meaning and its materialization in everyday life.
Enthymemes And Topoi In Dialogue
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Author : Ellen Breitholtz
language : en
Publisher: BRILL
Release Date : 2020-11-23
Enthymemes And Topoi In Dialogue written by Ellen Breitholtz and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with Language Arts & Disciplines categories.
In Enthymemes and Topoi in Dialogue, Ellen Breitholtz presents a novel and precise account of reasoning from an interactional perspective. The account draws on the concepts of enthymemes and topoi, originating in Aristotelian rhetoric and dialectic, and integrates these in a formal dialogue semantic account using TTR, a type theory with records. Argumentation analysis and formal approaches to reasoning often focus the logical validity of arguments on inferences made in discourse from a god’s-eye perspective. In contrast, Breitholtz’s account emphasises the individual perspectives of interlocutors and the function and acceptability of their reasoning in context. This provides an analysis of interactions where interlocutors have access to different topoi and therefore make different inferences.
Higher Orbifolds And Deligne Mumford Stacks As Structured Infinity Topoi
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Author : David Carchedi
language : en
Publisher: American Mathematical Soc.
Release Date : 2020
Higher Orbifolds And Deligne Mumford Stacks As Structured Infinity Topoi written by David Carchedi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Education categories.
The author develops a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. He chooses to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie, but his approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, which extends to derived and spectral Deligne-Mumford stacks as well.
Topoi
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Author : Robert Goldblatt
language : en
Publisher: Dover Publications
Release Date : 2013-12-23
Topoi written by Robert Goldblatt and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-23 with categories.
A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally. Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.