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. Pumplün in Zbl 0437.18001.

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. Pumplün in Zbl 0437.18001.

##### MSC:

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 |