Section 4.5 (00FT): The Smash Product of Pointed Sets

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Style 1	`book`	Alegreya Sans	`tcbthm`
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Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

4.5 The Smash Product of Pointed Sets

Subsection 4.5.1: Foundations
- Definition 4.5.1.1.1: Smash Products of Pointed Sets
- Remark 4.5.1.1.2: Unwinding Definition 4.5.1.1.1: The Universal Property I
- Remark 4.5.1.1.3: Unwinding Definition 4.5.1.1.1: The Universal Property II
- Construction 4.5.1.1.4: Smash Products of Pointed Sets
- Remark 4.5.1.1.5: On the Construction of the Smash Product of Pointed Sets
- Notation 4.5.1.1.6: Elements of Smash Products of Pointed Sets
- Remark 4.5.1.1.7: Basepoints of Smash Products of Pointed Sets
- Example 4.5.1.1.8: Examples of Smash Products of Pointed Sets
- Proposition 4.5.1.1.9: Properties of Smash Products of Pointed Sets
Subsection 4.5.2: The Internal Hom of Pointed Sets
- Definition 4.5.2.1.1: The Internal Hom of Pointed Sets
- Proposition 4.5.2.1.2: Properties of the Internal Hom of Pointed Sets
Subsection 4.5.3: The Monoidal Unit
- Definition 4.5.3.1.1: The Monoidal Unit of $\wedge $
Subsection 4.5.4: The Associator
- Definition 4.5.4.1.1: The Associator of $\wedge $
Subsection 4.5.5: The Left Unitor
- Definition 4.5.5.1.1: The Left Unitor of $\wedge $
Subsection 4.5.6: The Right Unitor
- Definition 4.5.6.1.1: The Right Unitor of $\wedge $
Subsection 4.5.7: The Symmetry
- Definition 4.5.7.1.1: The Symmetry of $\wedge $
Subsection 4.5.8: The Diagonal
- Definition 4.5.8.1.1: The Diagonal of $\wedge $
- Proposition 4.5.8.1.2: Properties of the Diagonal of $\wedge $
Subsection 4.5.9: The Monoidal Structure on Pointed Sets Associated to $\wedge $
- Proposition 4.5.9.1.1: The Monoidal Structure on Pointed Sets Associated to $\wedge $
Subsection 4.5.10: Universal Properties of the Smash Product of Pointed Sets I
- Theorem 4.5.10.1.1: Universal Properties of the Smash Product of Pointed Sets I
Subsection 4.5.11: Universal Properties of the Smash Product of Pointed Sets II
- Theorem 4.5.11.1.1: Universal Properties of the Smash Product of Pointed Sets II
Subsection 4.5.12: Monoids With Respect to the Smash Product of Pointed Sets
- Proposition 4.5.12.1.1: Monoids With Respect to $\wedge $
Subsection 4.5.13: Comonoids With Respect to the Smash Product of Pointed Sets
- Proposition 4.5.13.1.1: Comonoids With Respect to $\wedge $

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