Categorical foundations: special topics in order, topology, algebra, and sheaf theory, Vol. 97

By:

Pedicchio, Maria Cristina (Ed.)

Contributor(s):

Tholen, Walter (Ed.)

Series: Encyclopedia of mathematics and its applicationsPublication details: Cambridge University Press, 2004. New York:Description: xii; 417 p. hb; 24 cmISBN:

9780521834148

Subject(s):

DDC classification:

511.3 PED

Summary: 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 most 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 independent chapters, the reader will encounter various ways of how to study "spaces": order-theoretically via their open-set lattices, as objects of a fairly abstract category via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, "algebras" are treated as both models for Lawvere's algebraic theories and Eilenberg-Moore 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 that, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance, on the exponentiality of spaces and embeddability of algebras. Suggestions for further studies and research are also given.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	511.3 PED (Browse shelf(Opens below))	1	Available		028986

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 most 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 independent chapters, the reader will encounter various ways of how to study "spaces": order-theoretically via their open-set lattices, as objects of a fairly abstract category via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, "algebras" are treated as both models for Lawvere's algebraic theories and Eilenberg-Moore 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 that, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance, on the exponentiality of spaces and embeddability of algebras. Suggestions for further studies and research are also given.

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