zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Category theory. (English) Zbl 1100.18001
Oxford Logic Guides 49. Oxford: Oxford Science Publications. Oxford: Oxford University Press (ISBN 0-19-856861-4/hbk). xi, 256 p. £ 65.00 (2006).

Those with an interest in logic, linguistics, cognitive science, mathematics, computer science, philosophy, or a number of other fields, can deepen their appreciation of their subject having a working knowledge of category theory. This book is written for such people when their backgrounds include only a couple of tertiary mathematics or logic courses; say, a discrete mathematics course. Intuitive set theory, including the notion of function, is assumed. Structures such as topological spaces and rings are not avoided; they are there for those who know about them or care to learn elsewhere, but these bits are not essential to the development. The author concentrates more on ordered sets, monoids and groups, and the reader will develop some skill in dealing with those structures, as well as categories, by the end of the book.

The first half of the book gives the definition of category and then discusses concepts that live within one: these include epimorphisms, terminal objects, products, groups, limits, exponentials, and duality. Right in the middle of the book, functors are defined followed by natural transformations in the same chapter.

The second half goes on to deal with presheaf categories, adjoint functors, and monads. Features of the book include glimpses of typed lambda-calculus, elementary toposes, quantifiers as adjoints, and algebras for endofunctors. The author’s decade of teaching this material has produced a volume to enlighten the many who are mathematically competent but largely untested. The typeface is pleasant and the length (circa 260 pages) quite reasonable: an attractive text.


MSC:
18-01Textbooks (category theory)
03-01Textbooks (mathematical logic)