Download or read book Topoi written by R. Goldblatt and published by Elsevier. This book was released on 2014-06-28 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Model Theory and Topoi written by F.W. Lawvere and published by Springer. This book was released on 2006-11-15 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Collection of Lectures by Variuos Authors
Download or read book Transforming Topoi written by Andrew James Johnston and published by V&R Unipress. This book was released on 2018-09-10 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Enthymemes and Topoi in Dialogue written by Ellen Breitholtz and published by BRILL. This book was released on 2020-11-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Higher Orbifolds and Deligne Mumford Stacks as Structured Infinity Topoi written by David Carchedi and published by American Mathematical Soc.. This book was released on 2020 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Classifying Spaces and Classifying Topoi written by Izak Moerdijk and published by Springer. This book was released on 2006-11-14 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lecture Notes on Topoi and Quasitopoi written by Oswald Wyler and published by World Scientific. This book was released on 1991 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Forcing and Classifying Topoi written by Andrej Ščedrov and published by American Mathematical Soc.. This book was released on 1984 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Expressions of Sceptical Topoi in Late Antique Judaism written by Reuven Kiperwasser and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-19 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series Studies and Texts in Scepticism contains monographs, translations, and collected essays exploring scepticism in its dual manifestation as a purely philosophical tradition and as a set of sceptical strategies, concepts, and attitudes in the cultural field - especially in religions, perhaps most notably in Judaism. In such cultural contexts scepticism manifests as a critical attitude towards different dimensions and systems of secular or revealed knowledge and towards religious and political authorities. It is not merely an intellectual or theoretical worldview, but a critical form of life that expresses itself in such diverse phenomena as religion, literature, and society. Further book series of the Maimonides Centre for Advanced Studies are Jewish Thought, Philosophy, and Religion and the Yearbook of the Maimonides Centre for Advances Studies.
Download or read book A Companion to Greek Literature written by Martin Hose and published by John Wiley & Sons. This book was released on 2020-02-11 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Companion to Greek Literature presents a comprehensive introduction to the wide range of texts and literary forms produced in the Greek language over the course of a millennium beginning from the 6th century BCE up to the early years of the Byzantine Empire. Features contributions from a wide range of established experts and emerging scholars of Greek literature Offers comprehensive coverage of the many genres and literary forms produced by the ancient Greeks—including epic and lyric poetry, oratory, historiography, biography, philosophy, the novel, and technical literature Includes readings that address the production and transmission of ancient Greek texts, historic reception, individual authors, and much more Explores the subject of ancient Greek literature in innovative ways
Download or read book Ars Topica written by Sara Rubinelli and published by Springer Science & Business Media. This book was released on 2009-04-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ars Topica is the first full-length study of the nature and development of topoi, the conceptual ancestors of modern argument schemes, between Aristotle and Cicero. Aristotle and Cicero configured topoi in a way that influenced the subsequent tradition. Their work on the topos-system grew out of an interest in creating a theory of argumentation which could stand between the rigour of formal logic and the emotive potential of rhetoric. This system went through a series of developments and transformations resulting from the interplay between the separate aims of gaining rhetorical effectiveness and of maintaining dialectical standards. Ars Topica presents a comprehensive treatment of Aristotle’s and Cicero’s methods of topoi and, by exploring their relationship, it illuminates an area of ancient rhetoric and logic which has been obscured for more than two thousand years. Through an interpretation which is philologically rooted in the historical context of topoi, the book lays the ground for evaluating the relevance of the classical approaches to modern research on arguments, and at the same time provides an introduction to Greek and Roman theory of argumentation focussed on its most important theoretical achievements.
Download or read book Elementary Categories Elementary Toposes written by Colin McLarty and published by Clarendon Press. This book was released on 1992-06-04 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -
Download or read book Text as Topos in Religious Literature of the Spanish Golden Age written by M. Louise Salstad and published by Unc Department of Romance Studies. This book was released on 1995 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central component of this study is an index of the numerous motifs through which topoi of the text as symbol are articulated in the religious poetry, sermons, and sacramental plays of Golden Age Spain. Paired with the index is an anthology of the texts on which the book is based. In her introduction, Louise Salstad discusses the transmission and transformation of the topoi as they appear in the Old and New Testaments, classical literature, church writings, and medieval texts, and she considers the influence of the contemporary milieu on the shaping of these motifs. The book also includes an explanatory introduction to the index, biographical notes on authors, a chronology of works, a bibliography, and key word indexes of motifs in English and Spanish. The most extensive investigation of specific topoi undertaken in Spanish studies, this book will also be of interest to art historians and cultural historians whose focus is theology, the history of spirituality, or the history of the book.
Download or read book First Order Categorical Logic written by M. Makkai and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Higher Topos Theory AM 170 written by Jacob Lurie and published by Princeton University Press. This book was released on 2009-07-06 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. 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. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
Download or read book Diversity Competence written by Edwin Hoffman and published by CABI. This book was released on 2019-03-29 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a generous amount of theory on intercultural communication and competence in the context of international or multicultural environments. It describes what diversity competence entails and demonstrates how the TOPOI model offers an approach to analysing and addressing potential miscommunication. The book has 11 chapters.
Download or read book Order and Recursion in Topoi written by Tim Brook and published by . This book was released on 1977 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
