3 Monoidal Structures on the Category of Sets
This chapter contains some material on monoidal structures on
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Section 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
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Subsection 3.1.3: The Monoidal Unit
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Definition 3.1.3.1.1: The Monoidal Unit of
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Definition 3.1.3.1.1: The Monoidal Unit of
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Subsection 3.1.4: The Associator
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Definition 3.1.4.1.1: The Associator of
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Definition 3.1.4.1.1: The Associator of
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Subsection 3.1.5: The Left Unitor
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Definition 3.1.5.1.1: The Left Unitor of
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Definition 3.1.5.1.1: The Left Unitor of
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Subsection 3.1.6: The Right Unitor
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Definition 3.1.6.1.1: The Right Unitor of
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Definition 3.1.6.1.1: The Right Unitor of
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Subsection 3.1.7: The Symmetry
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Definition 3.1.7.1.1: The Symmetry of
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Definition 3.1.7.1.1: The Symmetry of
- Subsection 3.1.8: The Diagonal
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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
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Subsection 3.1.10: The Universal Property of
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Theorem 3.1.10.1.1: The Universal Property of
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Corollary 3.1.10.1.2: A Second Universal Property for
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Theorem 3.1.10.1.1: The Universal Property of
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Section 3.2: The Monoidal Category of Sets and Coproducts
- Subsection 3.2.1: Coproducts of Sets
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Subsection 3.2.2: The Monoidal Unit
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Definition 3.2.2.1.1: The Monoidal Unit of
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Definition 3.2.2.1.1: The Monoidal Unit of
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Subsection 3.2.3: The Associator
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Definition 3.2.3.1.1: The Associator of
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Definition 3.2.3.1.1: The Associator of
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Subsection 3.2.4: The Left Unitor
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Definition 3.2.4.1.1: The Left Unitor of
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Definition 3.2.4.1.1: The Left Unitor of
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Subsection 3.2.5: The Right Unitor
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Definition 3.2.5.1.1: The Right Unitor of
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Definition 3.2.5.1.1: The Right Unitor of
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Subsection 3.2.6: The Symmetry
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Definition 3.2.6.1.1: The Symmetry of
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Definition 3.2.6.1.1: The Symmetry of
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Subsection 3.2.7: The Monoidal Category of Sets and Coproducts
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Proposition 3.2.7.1.1: The Monoidal Structure on Sets Associated to
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Proposition 3.2.7.1.1: The Monoidal Structure on Sets Associated to
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Section 3.3: The Bimonoidal Category of Sets, Products, and Coproducts
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Subsection 3.3.1: The Left Distributor
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Definition 3.3.1.1.1: The Left Distributor of
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Definition 3.3.1.1.1: The Left Distributor of
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Subsection 3.3.2: The Right Distributor
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Definition 3.3.2.1.1: The Right Distributor of
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Definition 3.3.2.1.1: The Right Distributor of
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Subsection 3.3.3: The Left Annihilator
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Definition 3.3.3.1.1: The Left Annihilator of
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Definition 3.3.3.1.1: The Left Annihilator of
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Subsection 3.3.4: The Right Annihilator
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Definition 3.3.4.1.1: The Right Annihilator of
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Definition 3.3.4.1.1: The Right Annihilator of
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Subsection 3.3.5: The Bimonoidal Category of Sets, Products, and Coproducts
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Proposition 3.3.5.1.1: The Bimonoidal Structure on Sets Associated to
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Proposition 3.3.5.1.1: The Bimonoidal Structure on Sets Associated to
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Subsection 3.3.1: The Left Distributor
