The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo- topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo- logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).

Calculus of Fractions and Homotopy Theory

Science & Math

Gabriel, Peter

Zisman, M.

Mathematics

Springer

In this collection of quotations Peter Gabriel talks about his life and music from his days as lead singer with Genesis to his solo career. He discusses his spectacular live concerts, his involvement in the Womad Festival, and his support for the Anti-Apartheid Movement.

Peter Gabriel: In His Own Words

St.Michael, Mick

Michael, Mick St.

Humor & Entertainment

Omnibus Pr & Schirmer Trade Books

Hochschulunterricht für Mathematiker ist meist abstrakt und führt vom Allgemeinen zum Speziellen. Dieses Lehrbuch verfährt umgekehrt - von zwei Spezialfällen zur Allgemeinheit. Es erläutert zunächst Beweise der abstrakten Algebra am konkreten Beispiel der Matrizen und beleuchtet dann die Elementargeometrie. So bereitet es Lernende auf die "geometrische" Sprache der linearen Algebra am Ende des Buches vor. Plus: Beispiele, historische Kommentare.

Matrizen, Geometrie, Lineare Algebra (Birkhäuser Advanced Texts Basler Lehrbücher) (German Edition)

Birkhauser

Lokal Präsentierbare Kategorien/ Locally Presentable Categories (Lecture Notes in Mathematics, 221) (German Edition)

Representations of Finite-Dimensional Algebras (Encyclopaedia of Mathematical Sciences, 73)

Roiter, Andrei V.

From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." --The Mathematical Gazette

The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo­ topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo­ logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category ,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).

The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category ,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).

Calculus of Fractions and Homotopy Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 35)

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Books by Gabriel, Peter

See the best price to sell, buy, or rent books by Gabriel, Peter. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Calculus of Fractions and Homotopy Theory

Peter Gabriel: In His Own Words

Matrizen, Geometrie, Lineare Algebra (Birkhäuser Advanced Texts Basler Lehrbücher) (German Edition)

Lokal Präsentierbare Kategorien/ Locally Presentable Categories (Lecture Notes in Mathematics, 221) (German Edition)

Representations of Finite-Dimensional Algebras (Encyclopaedia of Mathematical Sciences, 73)

Representations of Finite-Dimensional Algebras (Encyclopaedia of Mathematical Sciences, 73)

Calculus of Fractions and Homotopy Theory

Calculus of Fractions and Homotopy Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 35)

Matrizen, Geometrie, Lineare Algebra (Birkhäuser Advanced Texts Basler Lehrbücher) (German Edition)