15 Notes

This chapter contains some notes.

• Section 15.1: TikZ Code for Commutative Diagrams
  • Subsection 15.1.1: Product Diagram With Circular Arrows
  • Subsection 15.1.2: Coproduct Diagram With Circular Arrows
  • Subsection 15.1.3: Cube Diagram
  • Subsection 15.1.4: Cube Diagram With Labelled Faces
  • Subsection 15.1.5: Pentagon Diagram
  • Subsection 15.1.6: Hexagon Diagram
  • Subsection 15.1.7: Double Square Diagram
  • Subsection 15.1.8: Double Hexagon Diagram
• Section 15.2: Retired Tags
  • Subsection 15.2.1: Relations
    • Oldtag 15.2.1.1.1: Equivalent Definitions of Relations
    • Oldtag 15.2.1.1.2: Interaction Between Composition and Characteristic Relations
    • Oldtag 15.2.1.1.3: Interaction Between Composition and Characteristic Relations
    • Oldtag 15.2.1.1.4: Explicit Description of Internal Left Kan Extensions Along Functions
    • Oldtag 15.2.1.1.5: Explicit Description of Internal Left Kan Lifts Along Functions
    • Oldtag 15.2.1.1.6: Internal Kan Extensions and Lifts
    • Oldtag 15.2.1.1.7: Internal Kan Extensions and Lifts
    • Oldtag 15.2.1.1.8: Internal Kan Extensions and Lifts
    • Oldtag 15.2.1.1.9: Better Characterisations of Representably Full Morphisms in $\boldsymbol {\mathsf{Rel}}$
    • Oldtag 15.2.1.1.10: Better Characterisations of Corepresentably Full Morphisms in $\boldsymbol {\mathsf{Rel}}$
    • Oldtag 15.2.1.1.11: Characterisation of Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.12: Characterisation of 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.13: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.14: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.15: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.16: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.17: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.18: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.19: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.20: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.21: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.22: 2-Categorical Monomorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.23: Characterisation of Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.24: Characterisation of Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.25: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.26: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.27: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.28: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.29: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.30: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.31: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.32: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.33: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.34: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.35: 2-Categorical Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.36: Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.37: Epimorphisms in $\mathsf{Rel}$
    • Oldtag 15.2.1.1.38: Interaction With Inverse Images II
    • Oldtag 15.2.1.1.39: Interaction With Coinverse Images II
  • Subsection 15.2.2: Pointed Sets
    • Oldtag 15.2.2.1.1: The Underlying Pointed Set of a Semimodule
    • Oldtag 15.2.2.1.2: The Underlying Pointed Set of a Module
  • Subsection 15.2.3: Tensor Products of Pointed Sets
    • Oldtag 15.2.3.1.1: Section on Universal Properties of the Smash Product of Pointed Sets I
    • Oldtag 15.2.3.1.2: Section on Universal Properties of the Smash Product of Pointed Sets II
    • Oldtag 15.2.3.1.3: Universal Properties of the Smash Product of Pointed Sets I
    • Oldtag 15.2.3.1.4: Universal Properties of the Smash Product of Pointed Sets II
  • Subsection 15.2.4: Categories
    • Oldtag 15.2.4.1.1: Picturing Natural Transformations in Diagrams
    • Oldtag 15.2.4.1.2: Interaction Between Fullness and Postcomposition Functors
• Section 15.3: Miscellany
  • Subsection 15.3.1: List of Things To Explore/Add
    • Remark 15.3.1.1.1: Things To Explore/Add