The Clowder Project

4.4 The Right Tensor Product of Pointed Sets

• Subsection 4.4.1: Foundations
  • Definition 4.4.1.1.1: The Right Tensor Product of Pointed Sets
  • Remark 4.4.1.1.2: Unwinding Definition 4.4.1.1.1: Universal Property I
  • Remark 4.4.1.1.3: Unwinding Definition 4.4.1.1.1: Universal Property II
  • Construction 4.4.1.1.4: The Right Tensor Product of Pointed Sets
  • Notation 4.4.1.1.5: Elements of Right Tensor Products of Pointed Sets
  • Remark 4.4.1.1.6: Basepoints of Right Tensor Products of Pointed Sets
  • Proposition 4.4.1.1.7: Properties of Right Tensor Products of Pointed Sets
  • Remark 4.4.1.1.8: On the Failure of $-\rhd Y$ To Be a Left Adjoint
• Subsection 4.4.2: The Right Internal Hom of Pointed Sets
  • Definition 4.4.2.1.1: The Right Internal Hom of Pointed Sets
  • Remark 4.4.2.1.2: Unwinding Definition 4.4.2.1.1, I: Comparison With $\smash {\webleft [-,-\webright ]^{\lhd }_{\mathsf{Sets}_{*}}}$
  • Remark 4.4.2.1.3: Unwinding Definition 4.4.2.1.1, II: Universal Property
  • Remark 4.4.2.1.4: Unwinding Definition 4.4.2.1.1, III: Explicit Description
  • Proposition 4.4.2.1.5: Properties of Right Internal Homs of Pointed Sets
• Subsection 4.4.3: The Right Skew Unit
  • Definition 4.4.3.1.1: The Right Skew Unit of $\rhd $
• Subsection 4.4.4: The Right Skew Associator
  • Definition 4.4.4.1.1: The Right Skew Associator of $\rhd $
  • Remark 4.4.4.1.2: Unwinding Definition 4.4.4.1.1
  • Remark 4.4.4.1.3: Non-Invertibility of the Skew Associator of $\rhd $
• Subsection 4.4.5: The Right Skew Left Unitor
  • Definition 4.4.5.1.1: The Right Skew Left Unitor of $\rhd $
  • Remark 4.4.5.1.2: Unwinding Definition 4.4.5.1.1
  • Remark 4.4.5.1.3: Non-Invertibility of the Skew Left Unitor of $\rhd $
• Subsection 4.4.6: The Right Skew Right Unitor
  • Definition 4.4.6.1.1: The Right Skew Right Unitor of $\rhd $
  • Remark 4.4.6.1.2: Unwinding Definition 4.4.6.1.1
  • Remark 4.4.6.1.3: Non-Invertibility of the Skew Right Unitor of $\rhd $
• Subsection 4.4.7: The Diagonal
  • Definition 4.4.7.1.1: The Diagonal of $\rhd $
• Subsection 4.4.8: The Right Skew Monoidal Structure on Pointed Sets Associated to $\rhd $
  • Proposition 4.4.8.1.1: The Right Skew Monoidal Structure on Pointed Sets Associated to $\rhd $
• Subsection 4.4.9: Monoids With Respect to the Right Tensor Product of Pointed Sets
  • Proposition 4.4.9.1.1: Monoids With Respect to $\rhd $