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Author:
Publisher:
ISBN:
Category : Geometry, Differential
Languages : en
Pages : 780
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Book Description
Author:
Publisher:
ISBN:
Category : Geometry, Differential
Languages : en
Pages : 780
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Geometry, Differential
Languages : en
Pages : 464
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Book Description
Author: Fosco Loregian
Publisher: Cambridge University Press
ISBN: 1108788602
Category : Mathematics
Languages : en
Pages : 332
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Book Description
The language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.
Author: L. Tamássy
Publisher: Springer Science & Business Media
ISBN: 9400901496
Category : Mathematics
Languages : en
Pages : 427
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Book Description
Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary, July 26-30, 1994
Author: Raghib Abu-saris
Publisher: World Scientific
ISBN: 9814490342
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This volume covers a wide range of areas in mathematics and mathematics education. There is emphasis on applied mathematics, including partial differential equations, dynamical systems, and difference equations. Other areas represented include algebra and number theory, statistics, and issues in mathematics education.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Author: Kouei Sekigawa
Publisher: World Scientific
ISBN: 9814548952
Category :
Languages : en
Pages : 158
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Book Description
The primary focus of this workshop concerns the interplay between the rich variety of structures and infinitesimal methods. The topics included in the volume are complex and harmonic analysis, complex algebraic geometry, differential geometry, mathematical physics and topology.
Author: Kouei Sekigawa
Publisher: World Scientific
ISBN: 9814549843
Category :
Languages : en
Pages : 234
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Book Description
The geometry of almost complex structures is fundamentally concerned with complex analysis and also mathematical physics. In view of the increasing interest in almost complex structures, this volume will be useful in future studies of geometry and complex analysis, and related fields.
Author: Colin McLarty
Publisher: Clarendon Press
ISBN: 0191589497
Category :
Languages : en
Pages : 282
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Book Description
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. -
Author: Robin Milner
Publisher: MIT Press
ISBN: 9780262161886
Category : Computers
Languages : en
Pages : 748
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Book Description
This collection of essays reflects the breadth of research in computer science. Following a biography of Robin Milner it contains sections on semantic foundations; programming logic; programming languages; concurrency; and mobility.
Author: Claudia Centazzo
Publisher: Presses univ. de Louvain
ISBN: 9782930344782
Category : Science
Languages : en
Pages : 200
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Book Description
Algebraic theories and algebraic categories offer an innovative and revelatory description of the syntax and the semantics. An algebraic theory is a concrete mathematical object -- the concept -- namely a set of variables together with formal symbols and equalities between these terms; stated otherwise, an algebraic theory is a small category with finite products. An algebra or model of the theory is a set-theoretical interpretation -- a possible meaning -- or, more categorically, a finite product-preserving functor from the theory into the category of sets. We call the category of models of an algebraic theory an algebraic category. By generalising the theory we do generalise the models. This concept is the fascinating aspect of the subject and the reference point of our project. We are interested in the study of categories of models. We pursue our task by considering models of different theories and by investigating the corresponding categories of models they constitute. We analyse localizations (namely, fully faithful right adjoint functors whose left adjoint preserves finite limits) of algebraic categories and localizations of presheaf categories. These are still categories of models of the corresponding theory.We provide a classification of localizations and a classification of geometric morphisms (namely, functors together with a finite limit-preserving left adjoint), in both the presheaf and the algebraic context.
