Preface |
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xi | |
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PART I DEVELOPMENT OF PHYSICAL CONCEPTS |
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3 | (86) |
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3 | (15) |
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1.2 Electromagnetism and Light |
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18 | (17) |
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1.3 Atomic Theory of Matter |
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35 | (16) |
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1.4 Radiation and Thermodynamics |
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51 | (14) |
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65 | (14) |
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1.6 The Mysterious Quantum |
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79 | (3) |
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1.7 Emission Origin for a Wave of Quanta |
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82 | (7) |
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89 | (34) |
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89 | (8) |
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97 | (5) |
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2.3 Problem of the Constancy of the Speed of Light |
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102 | (1) |
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2.4 Einstein's Relative Time |
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103 | (1) |
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2.5 Measuring the Speed of Light |
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103 | (2) |
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105 | (1) |
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2.7 General Principle of Relativity |
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106 | (5) |
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2.8 Universal Principle of Relativity |
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111 | (5) |
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2.9 A Light Quantum in Universal Relativity |
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116 | (7) |
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123 | (12) |
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3.1 Doppler Effect in Light |
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123 | (1) |
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3.2 Derivation of the Doppler Shift |
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124 | (2) |
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3.3 Difficulty with Special Relativity |
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126 | (1) |
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3.4 Doppler Shift Formulas with Acceleration |
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127 | (4) |
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3.5 Doppler Analysis with Acceleration |
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131 | (4) |
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PART II CATEGORY THEORY AND UNIVERSAL RELATIVITY |
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135 | (32) |
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135 | (1) |
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136 | (2) |
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4.3 Partial Binary Algebra of Arrows |
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138 | (1) |
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4.4 Definitions of a Category |
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139 | (6) |
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4.5 Some Standard Nomenclature about Categories |
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145 | (2) |
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4.6 Some Examples of Categories |
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147 | (6) |
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153 | (3) |
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156 | (1) |
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4.9 Generating New Categories from Those Existing |
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157 | (7) |
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158 | (1) |
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4.9.2 Slice or Comma Category |
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159 | (1) |
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160 | (1) |
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161 | (1) |
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4.9.5 Product and Sum Categories |
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162 | (1) |
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4.9.6 Category of Families of Objects of a Category |
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163 | (1) |
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4.10 Categories Presented as Diagrams |
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164 | (1) |
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165 | (2) |
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5 Properties of Arrows and Objects |
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167 | (70) |
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167 | (1) |
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5.2 Diagram and Commuting Diagram |
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168 | (1) |
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5.3 Section and Retraction Arrows |
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169 | (2) |
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5.4 Isoarrow and Related Topics |
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171 | (4) |
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173 | (1) |
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5.4.2 Isomorphism-Dense Subcategory |
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173 | (1) |
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5.4.3 Isomorphism-Closed Subcategory |
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174 | (1) |
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5.5 Monoarrow and Related Topics |
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175 | (8) |
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175 | (2) |
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177 | (2) |
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179 | (2) |
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181 | (1) |
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5.5.5 Bidirectional Arrow |
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182 | (1) |
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5.6 Intersection and Co-intersection |
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183 | (1) |
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184 | (1) |
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5.8 Separator, Separating Set, and Coseparator |
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185 | (1) |
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5.9 Equalizer, Has Equalizer, and Coequalizer |
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185 | (8) |
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186 | (2) |
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5.9.2 Multiple Equalizers |
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188 | (1) |
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188 | (2) |
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190 | (1) |
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191 | (1) |
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192 | (1) |
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5.10 Constant and Co-constant Arrows |
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193 | (1) |
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5.11 Initial and Terminal Objects |
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193 | (1) |
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194 | (1) |
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194 | (5) |
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198 | (1) |
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199 | (2) |
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201 | (1) |
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5.15 Reflection Arrow and Co-reflection Arrow |
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201 | (5) |
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206 | (4) |
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206 | (1) |
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207 | (3) |
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210 | (1) |
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5.17 Product, Coproduct, and Biproduct |
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210 | (11) |
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5.18 Pullback and Push-Out |
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221 | (12) |
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5.18.1 Congruences and Pullbacks |
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230 | (2) |
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232 | (1) |
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232 | (1) |
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5.19 Subobject Classifier |
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233 | (2) |
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235 | (2) |
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237 | (58) |
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237 | (3) |
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6.1.1 Arrows Connecting Categories |
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237 | (2) |
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6.1.2 Dual Role of a Functor |
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239 | (1) |
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6.2 Some Examples of Functors |
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240 | (2) |
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6.3 Important Nomenclature about Functors |
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242 | (1) |
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6.4 Properties of Functors |
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243 | (6) |
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6.4.1 Preservation of Categorical Property by Functors |
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243 | (2) |
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6.4.2 Reflection of Categorical Property by Functors |
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245 | (2) |
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6.4.3 Isofunctor and Isomorphism of Categories |
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247 | (1) |
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6.4.4 Equivalence Functor |
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248 | (1) |
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6.5 Equivalence of Categories |
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249 | (4) |
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6.6 Functors and Subcategories |
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253 | (4) |
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6.6.1 Inclusion of a Subcategory |
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254 | (1) |
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6.6.2 Full Embedding of a Subcategory |
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255 | (1) |
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6.6.3 Subcategories of Subcategories |
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256 | (1) |
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6.6.4 Skeleton of a Category |
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256 | (1) |
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6.7 Some Relevant Conceptions |
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257 | (2) |
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6.7.1 Graph of a Category |
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257 | (1) |
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6.7.2 Internal and External Characterization |
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258 | (1) |
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6.8 Category of All Categories? |
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259 | (1) |
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6.9 Functors and Natural Transformations |
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259 | (6) |
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6.9.1 Natural Transformation and Natural Isomorphism |
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259 | (1) |
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6.9.2 Usual Product of Natural Transformations |
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260 | (1) |
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6.9.3 Star Product of Natural Transformations |
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261 | (2) |
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6.9.4 Law for the Interchange of the Usual Product and the Star Product of Natural Transformations |
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263 | (1) |
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264 | (1) |
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265 | (4) |
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269 | (1) |
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6.12 "Constant Functor" Functor, or CF-Functor |
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270 | (1) |
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271 | (9) |
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6.14 Functors Preserving and Reflecting Limits |
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280 | (5) |
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6.15 Representable Functors |
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285 | (1) |
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6.16 Elements and Yoneda's Results |
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286 | (9) |
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7 Universal Associations by Functors |
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295 | (14) |
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295 | (1) |
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7.2 Objects and Arrows: Properties vis-a-vis Functors |
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295 | (14) |
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7.2.1 Universal Associate and Universal Arrow |
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295 | (1) |
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7.2.2 Universal Coassociate and Universal Coarrow |
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296 | (1) |
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7.2.3 Functor-Generation of Objects |
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297 | (12) |
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8 Adjoint Functors and Adjoint Situations |
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309 | (10) |
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309 | (1) |
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8.2 Adjoint and Coadjoint Functors |
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310 | (1) |
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310 | (5) |
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8.4 Describing Adjunction |
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315 | (4) |
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319 | (20) |
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319 | (2) |
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321 | (3) |
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324 | (6) |
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330 | (2) |
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332 | (3) |
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9.6 Additivity and Measures |
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335 | (2) |
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337 | (2) |
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10 The Meaning of Universal Relativity |
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339 | (38) |
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339 | (2) |
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341 | (4) |
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10.2.1 Categorical Measures |
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342 | (2) |
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10.2.2 Additive Categories of Real Numbers |
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344 | (1) |
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10.3 Quantifiers of Motion |
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345 | (1) |
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10.3.1 Distance and Changes to Distance |
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345 | (1) |
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10.4 Physical Space Is 3D, Always! |
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346 | (6) |
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10.4.1 Geometry Is a Free Choice |
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347 | (1) |
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10.4.2 Vectors and Changes to Vectors |
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348 | (1) |
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349 | (3) |
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10.5 Physical Coordinate System |
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352 | (2) |
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10.6 Characteristics of "Individuality" of Objects |
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354 | (5) |
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10.7 Categorical Dynamics |
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359 | (4) |
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363 | (3) |
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10.9 Emission Origin for the Wave of Quanta |
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366 | (8) |
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10.9.1 Statistical Considerations |
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368 | (2) |
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10.9.2 Emission and Formation of Wave of Quanta |
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370 | (2) |
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372 | (2) |
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374 | (3) |
Epilogue |
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377 | (6) |
Appendix A Set Theoretical Foundations |
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383 | (8) |
Appendix B Propositional Calculus |
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391 | (8) |
Bibliography |
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399 | (6) |
Index |
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405 | |