A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various "refinements" of the...
A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each vol...
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental...
This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.
This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. N...
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience, the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit...
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors f...
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint...
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and syntheti...
A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various "refinements" of the...
A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each vol...
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental...
This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.
This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. N...
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience, the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit...
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors f...
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint...
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and syntheti...
