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  1. Home
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  3. Categorical Foundations
  • Cited by 4
Publisher:
Cambridge University Press
Online publication date:
November 2013
Print publication year:
2003
Online ISBN:
9781107340985
DOI:
https://doi.org/10.1017/CBO9781107340985
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets
Series:
Encyclopedia of Mathematics and its Applications (97)
Information

Book description

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': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as 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 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.

Reviews

‘The book will be very useful for graduate students and teachers, and inspiring for the researchers interested in the discussed topics as well as in category theory itself.‘

Source: EMS Newsletter

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