Categorical foundations : special topics in order, topology, algebra, and Sheaf theory [EBook] / edited by Maria Cristina Pedicchio, Walter Tholen.
Categorical foundations : special topics in order, topology, algebra, and Sheaf theory [EBook] / edited by Maria Cristina Pedicchio, Walter Tholen.
The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical ma...
Personal Name(s):  Pedicchio, M. C., (editor) 

Tholen, W., (editor)  
Imprint: 
Cambridge :
Cambridge University Press,
2004

Physical Description: 
1 online resource (xii, 417 pages) 
Note: 
englisch 
ISBN: 
9781107340985 9780521834148 
Series Title: 
Encyclopedia of mathematics and its applications ;
volume 97 
Subject (LOC):  
Full Text 
LEADER  02876nam a22003258i 4500  

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245  0  0  a Categorical foundations : b special topics in order, topology, algebra, and Sheaf theory h [EBook] / c edited by Maria Cristina Pedicchio, Walter Tholen. 
264  1  a Cambridge : b Cambridge University Press, c 2004 e (CUP) f CUP20200108  
300  a 1 online resource (xii, 417 pages)  
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490  a Encyclopedia of mathematics and its applications ; v volume 97  
500  a englisch  
505  0  0  t Ordered sets via adjunction / r R.J. Wood  t Locales / r Jorge Picado, Ale�s Pultr, and Anna Tozzi  t Functional approach to general topology / r Maria Manuel Clementino, Eraldo Giuli, and Walter Tholen  t Regular, protomodular, and Abelian categories / r Dominique Bourn and Marino Gran  t Aspects of monads / r John MacDonald and Manuela Sobral  t Algebraic categories / r Maria Cristina Pedicchio and Fabrizio Rovatti  t Sheaf theory / r Claudia Centazzo and Enrico M. Vitale  t Beyond Barr exactness / r George Janelidze, Manuela Sobral, and Walter Tholen. 
520  a The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': ordertheoretically via their openset lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of setvalued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as EilenbergMoore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance on the exponentiability of spaces and embeddability of algebras.  
650  0  a Categories (Mathematics)  
700  1  a Pedicchio, M. C., e editor  
700  1  a Tholen, W., e editor  
856  4  0  u https://doi.org/10.1017/CBO9781107340985 z Volltext 
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