The Clowder Project

3.3 The Bimonoidal Category of Sets, Products, and Coproducts

• Subsection 3.3.1: The Left Distributor
  • Definition 3.3.1.1.1: The Left Distributor of $\times $ over $\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}$
• Subsection 3.3.2: The Right Distributor
  • Definition 3.3.2.1.1: The Right Distributor of $\times $ over $\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}$
• Subsection 3.3.3: The Left Annihilator
  • Definition 3.3.3.1.1: The Left Annihilator of $\times $
• Subsection 3.3.4: The Right Annihilator
  • Definition 3.3.4.1.1: The Right Annihilator of $\times $
• Subsection 3.3.5: The Bimonoidal Category of Sets, Products, and Coproducts
  • Proposition 3.3.5.1.1: The Bimonoidal Structure on Sets Associated to $\times $ and $\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}$