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Author: Joël Biard Publisher: Peeters Publishers ISBN: 9789042913356 Category : Language Arts & Disciplines Languages : en Pages : 420
Book Description
Evoquees par Augustin, les Categories d'Aristote, accompagnees de l'introduction de Porphyre, sont traduites et commentees par Boece. Deja exposee dans le monde arabo-musulman, cette oeuvre devait faire l'objet de nombreux commentaires dans le monde latin, sans interruption, du temps d'Abelard jusqu'a la fin du Moyen Age. De l'etude du langage a la theorie de l'etre, ouvrant sur la philosophie naturelle et la theologie, les interrogations que suscitent les Categories sont multiformes. Elles concernent le statut des categories, leur nombre, les differents types de predication, ou la nature particuliere de certaines categories comme la relation ou la quantite. Le premier chapitre du traite, avec sa distinction entre equivoques, univoques et paronymes, suscite des reflexions sur les variations semantiques, les transferts de sens, et donne en meme temps naissance a la theorie de l'analogie de l'etant, aux implications metaphysiques et theologiques majeures. Les vingt deux essais de ce receuil explorent, a travers l'etude d'auteurs connus ou moins connus, les multiples facettes de cette riche tradition medievale de commentaires sur les Categories d'Aristote.
Author: Joël Biard Publisher: Peeters Publishers ISBN: 9789042913356 Category : Language Arts & Disciplines Languages : en Pages : 420
Book Description
Evoquees par Augustin, les Categories d'Aristote, accompagnees de l'introduction de Porphyre, sont traduites et commentees par Boece. Deja exposee dans le monde arabo-musulman, cette oeuvre devait faire l'objet de nombreux commentaires dans le monde latin, sans interruption, du temps d'Abelard jusqu'a la fin du Moyen Age. De l'etude du langage a la theorie de l'etre, ouvrant sur la philosophie naturelle et la theologie, les interrogations que suscitent les Categories sont multiformes. Elles concernent le statut des categories, leur nombre, les differents types de predication, ou la nature particuliere de certaines categories comme la relation ou la quantite. Le premier chapitre du traite, avec sa distinction entre equivoques, univoques et paronymes, suscite des reflexions sur les variations semantiques, les transferts de sens, et donne en meme temps naissance a la theorie de l'analogie de l'etant, aux implications metaphysiques et theologiques majeures. Les vingt deux essais de ce receuil explorent, a travers l'etude d'auteurs connus ou moins connus, les multiples facettes de cette riche tradition medievale de commentaires sur les Categories d'Aristote.
Author: Alexei Davydov Publisher: American Mathematical Soc. ISBN: 0821839705 Category : Mathematics Languages : en Pages : 482
Book Description
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.
Author: Giuseppe D' Anna Publisher: Georg Olms Verlag ISBN: 3487156571 Category : Philosophy Languages : en Pages : 272
Book Description
Das Nachdenken über die Kategorien markiert einen grundlegenden Übergang in der Geschichte der Philosophie. Durch die Theoretisierung dieses Problems erhält die Philosophie jenen metareflexiven Charakter, der wahrscheinlich eines der typischeren Merkmale philosophischen Wissens und ihrer Methode darstellt. Das Kategorienproblem wurde im Laufe der Geschichte der Philosophie schrittweise durchdrungen, aber nie endgültig gelöst. In dieser Hinsicht kann die Geschichte der Kategorien im Rahmen der Philosophie nicht als abgeschlossen gelten: tatsächlich wird das Kategorienthema vom Altertum bis in die Gegenwart hinein analysiert und diskutiert, ohne dass seine theoretische Fruchtbarkeit bereits erschöpft wäre. Die aktuelle Kategorienforschung muss sich unweigerlich mit der Geschichte der Kategorien befassen, wenn sie Fortschritte erzielen und bereits in der Vergangenheit begangene Fehler vermeiden will. Hieraus ergibt sich eine der Aufgaben des vorliegenden Bandes, der von dem Bedürfnis ausgeht, Perspektiven und Wege der Kategoriengeschichte aufzuzeigen. Das Ergebnis ist nicht erschöpfend; vielmehr wird ein erster und partieller Beitrag zu einem ausgedehnteren Projekt vorgelegt. The reflection upon the categories leaves a fundamental mark in the history of philosophy. By theorizing such issue, philosophy gains a meta-reflexive feature, which is probably one of the most distinguishing traits of this kind of knowledge, including its method. In the history of philosophy, the question of the categories has been gradually investigated and clarified but it still remains to be solved. Therefore, from a philosophical perspective, the history of the categories is far from coming to an end: since ancient times, it has been debated and discussed, thus revealing all its theoretical potential. Such a broad history should be taken into account by any present study that wants to represent a real progress in the research, in order to avoid repeating errors that have been already made in the past. Among other things, this is one of the objectives of the present volume, which comes from the will to describe some paths and perspectives of this history, without claiming to deliver an exhaustive overview and rather representing the first partial contribution to a wider project.
Author: P. Salmon Publisher: Springer Science & Business Media ISBN: 3642109799 Category : Mathematics Languages : en Pages : 341
Book Description
L. Badescu: Sur certaines singularités des variétés algébriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algébriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de séries formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all’algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces.
Author: Carlos Simpson Publisher: Cambridge University Press ISBN: 1139502190 Category : Mathematics Languages : en Pages : 653
Book Description
The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
Author: John C. Baez Publisher: Springer Science & Business Media ISBN: 1441915362 Category : Algebra Languages : en Pages : 292
Book Description
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Author: Joël Biard
Author: Joël Biard
Author: Alexei Davydov
Author: 
Author: Julia E. Bergner
Author: P.J. Hilton
Author: Giuseppe D' Anna
Author: P. Salmon
Author: Carlos Simpson
Author: Denis-Charles Cisinski
Author: John C. Baez