Author | Lane, Saunders Mac. author |
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Title | Categories for the Working Mathematician [electronic resource] / by Saunders Mac Lane |
Imprint | New York, NY : Springer New York, 1971 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9839-7 |
Descript | IX, 262 p. 14 illus. online resource |
I. Categories, Functors and Natural Transformations -- 1. Axioms for Categories -- 2. Categories -- 3. Functors -- 4. Natural Transformations -- 5. Monics, Epis, and Zeros -- 6. Foundations -- 7. Large Categories -- 8. Hom-sets -- II. Constructions on Categories -- 1. Duality -- 2. Contravariance and Opposites -- 3. Products of Categories -- 4. Functor Categories -- 5. The Category of All Categories -- 6. Comma Categories -- 7. Graphs and Free Categories -- 8. Quotient Categories -- III. Universals and Limits -- 1. Universal Arrows -- 2. The Yoneda Lemma -- 3. Coproducts and Colimits -- 4. Products and Limits -- 5. Categories with Finite Products -- 6. Groups in Categories -- IV. Adjoints -- 1. Adjunctions -- 2. Examples of Adjoints -- 3. Reflective Subcategories -- 4. Equivalence of Categories -- 5. Adjoints for Preorders -- 6. Cartesian Closed Categories -- 7. Transformations of Adjoints -- 8. Composition of Adjoints -- V. Limits -- 1. Creation of Limits -- 2. Limits by Products and Equalizers -- 3. Limits with Parameters -- 4. Preservation of Limits -- 5. Adjoints on Limits -- 6. Freydโs Adjoint Functor Theorem -- 7. Subobjects and Generators -- 8. The Special Adjoint Functor Theorem -- 9. Adjoints in Topology -- VI. Monads and Algebras -- 1. Monads in a Category -- 2. Algebras for a Monad -- 3. The Comparison with Algebras -- 4. Words and Free Semigroups -- 5. Free Algebras for a Monad -- 6. Split Coequalizers -- 7. Beckโs Theorem -- 8. Algebras are T-algebras -- 9. Compact Hausdorff Spaces -- VII. Monoids -- 1. Monoidal Categories -- 2. Coherence -- 3. Monoids -- 4. Actions -- 5. The Simplicial Category -- 6. Monads and Homology -- 7. Closed Categories -- 8. Compactly Generated Spaces -- 9. Loops and Suspensions -- VIII. Abelian Categories -- 1. Kernels and Cokernels -- 2. Additive Categories -- 3. Abelian Categories -- 4. Diagram Lemmas -- IX. Special Limits -- 1. Filtered Limits -- 2. Interchange of Limits -- 3. Final Functors -- 4. Diagonal Naturality -- 5. Ends -- 6. Coends -- 7. Ends with Parameters -- 8. Iterated Ends and Limits -- X. Kan Extensions -- 1. Adjoints and Limits -- 2. Weak Universality -- 3. The Kan Extension -- 4. Kan Extensions as Coends -- 5. Pointwise Kan Extensions -- 6. Density -- 7. All Concepts are Kan Extensions -- Table of Terminology