The Clowder Project

3.1 The Monoidal Category of Sets and Products

• Subsection 3.1.1: Products of Sets
• Subsection 3.1.2: The Internal Hom of Sets
• Subsection 3.1.3: The Monoidal Unit
  • Definition 3.1.3.1.1: The Monoidal Unit of $\times $
• Subsection 3.1.4: The Associator
  • Definition 3.1.4.1.1: The Associator of $\times $
• Subsection 3.1.5: The Left Unitor
  • Definition 3.1.5.1.1: The Left Unitor of $\times $
• Subsection 3.1.6: The Right Unitor
  • Definition 3.1.6.1.1: The Right Unitor of $\times $
• Subsection 3.1.7: The Symmetry
  • Definition 3.1.7.1.1: The Symmetry of $\times $
• Subsection 3.1.8: The Diagonal
  • Definition 3.1.8.1.1: The Diagonal of $\times $
  • Proposition 3.1.8.1.2: Properties of the Diagonal Map
• Subsection 3.1.9: The Monoidal Category of Sets and Products
  • Proposition 3.1.9.1.1: The Monoidal Structure on Sets Associated to the Product
• Subsection 3.1.10: The Universal Property of $\webleft (\mathsf{Sets},\times ,\text{pt}\webright )$
  • Theorem 3.1.10.1.1: The Universal Property of $\webleft (\mathsf{Sets},\times ,\text{pt}\webright )$
  • Corollary 3.1.10.1.2: A Second Universal Property for $\webleft (\mathsf{Sets},\times ,\text{pt}\webright )$