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CONTENTS ======== Preface 1. Categories 1 Definition of category 2 Functors 3 Natural transformations 4 Elements and Subobjects 5 The Yoneda Lemma 6 Pullbacks 7 Limits 8 Colimits 9 Adjoint functors 10 Filtered colimits 11 Notes to Chapter I 2. Toposes 63 1 Basic Ideas about Toposes 2 Sheaves on a Space 3 Properties of Toposes 4 The Beck Conditions 5 Notes to Chapter 2 3. Triples 83 1 Definition and Examples 2 The Kleisli and Eilenberg-Moore Categories 3 Tripleability 4 Properties of Tripleable Functors 5 Suficient Conditions for Tripleability 6 Morphisms of Triples 7 Adjoint Triples 8 Historical Notes on Triples 4. Theories 123 1 Sketches 2 The Ehresmann-Kennison Theorem 3 Finite-Product Theories 4 Left Exact Theories 5 Notes on Theories 5. Properties of Toposes 148 1 Tripleability of P 2 Slices of Toposes 3 Logical Functors 4 Toposes are Cartesian Closed 5 Exactness Properties of Toposes 6 The Heyting Algebra Structure on 6. Permanence Properties of Toposes 170 1 Topologies 2 Sheaves for a Topology 3 Sheaves form a topos 4 Left exact cotriples 5 Left exact triples 6 Categories in a Topos 7 Grothendieck Topologies 8 Giraud's Theorem 7. Representation Theorems 207 1 Freyd's Represen
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Common subject areas: history, science, philosophy, social sciences.
- Author
- Michael Barr, Charles Wells
- Publisher
- Springer New York; Springer
- Published
- 1985
- Language
- EN
- ISBN
- 9781489900234
- Category
- nonfiction
- Subjects
- Mathematics, Stem
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