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Subtlety in relativity

Author: Sanjay Moreshwar Wagh
Publisher: Singapore : Pan Stanford, ©2018.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sanjay Moreshwar Wagh
ISBN: 1351238299 9781351238298 1351238310 9781351238311 9781351238304 1351238302
OCLC Number: 1019666980
Description: 1 online resource (374) : illustrations
Contents: Machine generated contents note: pt. I DEVELOPMENT OF PHYSICAL CONCEPTS --
1. Light Quantum --
1.1. Wave Theory of Light --
1.2. Electromagnetism and Light --
1.3. Atomic Theory of Matter --
1.4. Radiation and Thermodynamics --
1.5. What Is a Quantum? --
1.6. Mysterious Quantum --
1.7. Emission Origin for a Wave of Quanta --
2. Idea of Relativity --
2.1. Galileo and Newton --
2.2. What Is Relativity? --
2.3. Problem of the Constancy of the Speed of Light --
2.4. Einstein's Relative Time --
2.5. Measuring the Speed of Light --
2.6. Time Is Absolute --
2.7. General Principle of Relativity --
2.8. Universal Principle of Relativity --
2.9. Light Quantum in Universal Relativity --
3. Doppler Effect --
3.1. Doppler Effect in Light --
3.2. Derivation of the Doppler Shift --
3.3. Difficulty with Special Relativity --
3.4. Doppler Shift Formulas with Acceleration --
3.5. Doppler Analysis with Acceleration --
pt. II CATEGORY THEORY AND UNIVERSAL RELATIVITY --
4. What Is a Category? --
4.1. Introduction --
4.2. Arrow --
4.3. Partial Binary Algebra of Arrows --
4.4. Definitions of a Category --
4.5. Some Standard Nomenclature about Categories --
4.6. Some Examples of Categories --
4.7. Duality Principle --
4.8. Subcategory --
4.9. Generating New Categories from Those Existing --
4.9.1. Quotient Category --
4.9.2. Slice or Comma Category --
4.9.3. Arrow Category --
4.9.4. Triangle Category --
4.9.5. Product and Sum Categories --
4.9.6. Category of Families of Objects of a Category --
4.10. Categories Presented as Diagrams --
4.11. Summary --
5. Properties of Arrows and Objects --
5.1. Introduction --
5.2. Diagram and Commuting Diagram --
5.3. Section and Retraction Arrows --
5.4. Isoarrow and Related Topics --
5.4.1. Isomorphic Objects --
5.4.2. Isomorphism-Dense Subcategory --
5.4.3. Isomorphism-Closed Subcategory --
5.5. Monoarrow and Related Topics --
5.5.1. Monoarrow --
5.5.2. Subobject --
5.5.3. Epiarrow --
5.5.4. Quotient Object --
5.5.5. Bidirectional Arrow --
5.6. Intersection and Co-intersection --
5.7. Factorization --
5.8. Separator, Separating Set, and Coseparator --
5.9. Equalizer, Has Equalizer, and Coequalizer --
5.9.1. Equalizer Arrow --
5.9.2. Multiple Equalizers --
5.9.3. Regular Monoarrow --
5.9.4. Extremal Monoarrow --
5.9.5. Strict Monoarrow --
5.9.6. Coequalizer --
5.10. Constant and Co-constant Arrows --
5.11. Initial and Terminal Objects --
5.12. Zero Object --
5.13. Zero Arrow --
5.13.1. Pointed Category --
5.14. Kernel Arrow --
5.14.1. Normal Monoarrow --
5.15. Reflection Arrow and Co-reflection Arrow --
5.16. Source and Sink --
5.16.1. Sources --
5.16.2. Monosources --
5.16.3. Sinks --
5.17. Product, Coproduct, and Biproduct --
5.18. Pullback and Push-Out --
5.18.1. Congruences and Pullbacks --
5.18.2. Push-Out --
5.18.3. Pullation Square --
5.19. Subobject Classifier --
5.20. Summary --
6. Functors --
6.1. Introduction --
6.1.1. Arrows Connecting Categories --
6.1.2. Dual Role of a Functor --
6.2. Some Examples of Functors --
6.3. Important Nomenclature about Functors --
6.4. Properties of Functors --
6.4.1. Preservation of Categorical Property by Functors --
6.4.2. Reflection of Categorical Property by Functors --
6.4.3. Isofunctor and Isomorphism of Categories --
6.4.4. Equivalence Functor --
6.5. Equivalence of Categories --
6.6. Functors and Subcategories --
6.6.1. Inclusion of a Subcategory --
6.6.2. Full Embedding of a Subcategory --
6.6.3. Subcategories of Subcategories --
6.6.4. Skeleton of a Category --
6.7. Some Relevant Conceptions --
6.7.1. Graph of a Category --
6.7.2. Internal and External Characterization --
6.8. Category of All Categories? --
6.9. Functors and Natural Transformations --
6.9.1. Natural Transformation and Natural Isomorphism --
6.9.2. Usual Product of Natural Transformations --
6.9.3. Star Product of Natural Transformations --
6.9.4. Law for the Interchange of the Usual Product and the Star Product of Natural Transformations --
6.9.5. Godement's Rules --
6.10. Functor Categories --
6.11. Evaluation Functor --
6.12. "Constant Functor" Functor, or CF-Functor --
6.13. Limits and Colimits --
6.14. Functors Preserving and Reflecting Limits --
6.15. Representable Functors --
6.16. Elements and Yoneda's Results --
7. Universal Associations by Functors --
7.1. Introduction --
7.2. Objects and Arrows: Properties vis-a-vis Functors --
7.2.1. Universal Associate and Universal Arrow --
7.2.2. Universal Coassociate and Universal Coarrow --
7.2.3. Functor-Generation of Objects --
8. Adjoint Functors and Adjoint Situations --
8.1. Introduction --
8.2. Adjoint and Coadjoint Functors --
8.3. Adjoint Situations --
8.4. Describing Adjunction --
9. Categorical Measures --
9.1. Introduction --
9.2. Preliminaries --
9.3. Additivity --
9.4. Category: Family (C) --
9.5. Category: pFamily(C) --
9.6. Additivity and Measures --
9.7. Summary --
10. Meaning of Universal Relativity --
10.1. Introduction --
10.2. Categorical Basis --
10.2.1. Categorical Measures --
10.2.2. Additive Categories of Real Numbers --
10.3. Quantifiers of Motion --
10.3.1. Distance and Changes to Distance --
10.4. Physical Space Is 3D, Always! --
10.4.1. Geometry Is a Free Choice --
10.4.2. Vectors and Changes to Vectors --
10.4.3. Motion and Time --
10.5. Physical Coordinate System --
10.6. Characteristics of "Individuality" of Objects --
10.7. Categorical Dynamics --
10.8. Inertialess Objects --
10.9. Emission Origin for the Wave of Quanta --
10.9.1. Statistical Considerations --
10.9.2. Emission and Formation of Wave of Quanta --
10.9.3. Remarks --
10.10. Concluding Remarks.
Responsibility: Sanjay Moreshwar Wagh.

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