Inhalt

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   Preface
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   Summary
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   Zusammenfassung
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   Contents
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   Chapter I. Introduction
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  Chapter II. Computability of categories
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   1. Computable functions and decidable sets
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   2. Categories with Hom-setoids
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   3. Categories with Hom-setoids vs. classical categories
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   4. Computable categories
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   5. Decidable properties
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   6. Preadditive categories
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   7. Additive categories
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   8. Preabelian categories
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   9. Abelian categories
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   10. Categorical notions
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  Chapter III. Implementation of graded modules
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   1. The category of graded module presentations
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   2. Computability of graded module presentations
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  Chapter IV. Generalized morphisms and Serre quotients
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   1. The category of generalized morphisms
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   2. Structure of the category of generalized morphisms
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   3. Generalized and pseudo-inverse
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   4. Serre quotients
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   5. Computability of Serre quotients
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  Chapter V. The category of coherent sheaves over a toric variety
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   1. Preliminaries from toric geometry
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   2. Equivalence of Serre quotient and coherent sheaves
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   3. Deciding membership of the kernel of the sheafification functor
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  Chapter VI. Application
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   1. Preliminaries
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   2. Bicomplexes
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   3. Internal Hom and Ext
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   4. Grade filtration
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   5. Spectral sequences
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   6. Filtered presentation
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   7. Coherent sheaves
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  Chapter VII. Implementation of computable categories
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   1. The concept of categorical programming
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   2. Main design goal and feature
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   3. Error messages for categorical operations
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   4. Undecidable realizations
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   5. Ensuring compatibility: WithGiven operations
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   6. Caching
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   7. Primitive and derived categorical operations
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   8. Logic Propagation: ToDoLists
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   Bibliography
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  Appendix A. Programming in Cap
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   1. An overview of installing categories
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   2. The category object
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   3. Functors and natural transformations: The category of categories
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   4. Special categories implemented in Cap
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  Appendix B. Logical theorems in Cap
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   1. Logic for all categories
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   2. Logic for preadditive categories
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   3. Logic for additive categories
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   4. Logic for abelian categories
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   Appendix C. All method names
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   Appendix D. Derivations
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   Appendix E. Final Derivations
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  Appendix F. Installed basic operations
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   1. Primitive operation index
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   2. Primitive operations for left module presentations
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   3. Primitive operations for right module presentations
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   4. Primitive operations for graded left module presentations
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   5. Primitive operations for graded right module presentations
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   6. Primitive operations for generalized morphisms by cospans
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   7. Primitive operations for generalized morphisms by spans
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   8. Primitive operations for generalized morphisms by three arrows
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   9. Primitive operations for Serre quotient by cospans
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   10. Primitive operations for Serre quotient by spans
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   11. Primitive operations for Serre quotient by three arrows
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  Appendix G. Application code
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   1. Function ResolutionFunctor
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   2. Function ResolutionFunctorToComplex
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   3. Function ResolutionFunctorToCocomplex
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   4. Function FreeResolutionComplex
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   5. Function FreeResolutionCocomplex
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   6. Function ResolutionTo
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   7. Function CAP INTERNAL HORSE SHOE HELPER
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   8. Function HorseShoeLemma
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   9. Function CartanEilenbergResolution
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   10. Function DualOnComplex
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   11. Function DualOnCocomplex
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   12. Function DualOnCochainMap
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   13. Function DualOnCocomplexCocomplex
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   14. Function TransposeComplexOfComplex
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   15. Function ResolutionLength
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   16. Function TotalComplexOfBicomplex
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   17. Function EmbeddingInObjectOfTotalComplex
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   18. Function ConnectingMorphismFromCocomplexToCartanEilenbergResolution
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   19. Function GeneralizedEmbeddingOfHomology
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   20. Function GeneralizedMorphismBetweenHomologies
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   21. Function GeneralizedEmbeddingOfSpectralSequenceEntry
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   22. Function PurityFiltrationBySpectralSequence
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   Index