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Category theory. An introduction. 3rd ed. (English) Zbl 1125.18300
Sigma Series in Pure Mathematics 1. Lemgo: Heldermann Verlag (ISBN 978-3-88538-001-6/hbk). xi, 382 p. (2007).
Publisher’s description: This is a by now classical text in mathematics. It gives an introduction to category theory assuming only minimal knowledge in set theory, algebra or topology. The book is designed for use during the early stages of graduate study – or for ambitious undergraduates. Each chapter contains numerous exercises for further study and control.
The attempt is made to present category theory mainly as a convenient language – one which ties together widespread notions, which puts many existing results in their proper perspective, and which provides a means for appreciation of the unity that exists in modern mathematics, despite the increasing tendencies toward fragmentation and specialization.
The fact that the book appears in a 3rd edition proves that the authors achieved their goals.
See the detailed review of the 2nd ed. by D. Pumpl√ľn in Zbl 0437.18001.

18-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18E05 Preadditive, additive categories
18E10 Abelian categories, Grothendieck categories
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18B05 Categories of sets, characterizations
18A25 Functor categories, comma categories
18A35 Categories admitting limits (complete categories), functors preserving limits, completions