Topoi for Physics

Contents

• Topos
  • Initial object
  • Terminal Object
  • Pullback
    • Examples of Pullback
  • Pushouts
  • Exponentiation
    • Examples of Exponentiation
  • Name of an arrow
  • Power object
  • Subobject Classifier
    • Subobjects
    • Examples of a Subobject
    • Definition of Subobject Classifier
  • What is a Subobject Classifier in Topos ?
    • Sieve
    • Elements of Subobject Classifier
    • Example of Yoneda's Lemma
  • Subobject Classifier in the Topos of Presheaves
  • Global sections
  • Local sections
  
  
• Presheaves in Quantum Mechanics
  • Spectral Presheaf on
    • Example of spectral presheaf
  • Dual Presheaf on
  • Dual Presheaf D o W
  • Coarse Graining Presheaf
    • Coarse graining presheaf G
    • Coarse Graining Presheaf on category of Boolean subalgebras
  • Example of Coarse Graining Presheaf
  
  
• Worked example of the Coarse Graining Presheaf