Author | Gabriel, Peter. author |
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Title | Calculus of Fractions and Homotopy Theory [electronic resource] / by Peter Gabriel, Michel Zisman |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1967 |
Connect to | http://dx.doi.org/10.1007/978-3-642-85844-4 |
Descript | X, 168 p. online resource |
Dictionary -- I. Categories of Fractions -- 1. Categories of Fractions. Categories of Fractions and Adjoint Functors -- 2. The Calculus of Fractions -- 3. Calculus of Left Fractions and Direct Limits -- 4. Return to Paragraph 1 -- II. Simplicial Sets -- 1. Functor Categories -- 2. Definition of Simplicial Sets -- 3. Skeleton of a Simplicial Set -- 4. Simplicial Sets and Category of Categories -- 5. Ordered Sets and Simplicial Sets. Shuffles -- 6. Groupoids -- 7. Groupoids and Simplicial Sets -- III. Geometric Realization of Simplicial Sets -- 1. Geometric Realization of a Simplicial Set -- 4. Kelley Spaces -- 3. Exactness Properties of the Geometric Realization Functor -- 4. Geometric Realization of a Locally Trivial Morphism -- IV. The Homotopic Category -- 1. Homotopies -- 2. Anodyne Extensions -- 3. Kan Complexes -- 4. Pointed Complexes -- 5. Poincarรฉ Group of a Pointed Complex -- V. Exact Sequences of Algebraic Topology -- 1. 2-Categories -- 2. Exact Sequences of Pointed Groupoids -- 3. Spaces of Loops -- 4. Exact Sequences: Statement of the Theorem and Invariance -- 5. Proof of Theorem 4.2 -- 6. Duality -- 7. First Example: Pointed Topological Spaces -- 8. Second Example: Differential Complexes of an Abelian Category -- VI. Exact Sequences of the Homotopic Category -- 1. Spaces of Loops -- 2. Cones -- 3. Homotopy Groups -- 4. Generalities on Fibrations -- 5. Minimal Fibrations -- VII. Combinatorial Description of Topological Spaces -- 1. Geometric Realization of the Homotopic Category -- 2. Geometric Realization of the Pointed Homotopic Category -- 3. Proof of Milnorโs Theorem -- Appendix I. Coverings -- 1. Coverings of a Groupoid -- 2. Coverings of Groupoids and Simplicial Coverings -- 3. Simplicial Coverings and Topological Coverings -- Appendix II. The Homology Groups of a Simplicial Set -- 2. The Reduced Homology Group of a Pointed Simplicial Set -- 3. The Spectral Sequence of Direct Limits -- 4. The Spectral Sequence of a Fibration -- Index of Notations -- Terminological Index