Item 4 (00C2) — The Clowder Project

Preferences

Font:

PDF Style:

Here's a breakdown of the differences between each PDF style:

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

Symmetric Strong Monoidality With Respect to Smash Products. The free pointed set functor of Item 1 has a symmetric strong monoidal structure
\[ \webleft (\webleft (-\webright )^{+},\webleft (-\webright )^{+,\times },\webleft (-\webright )^{+,\times }_{\mathbb {1}}\webright ) \colon \webleft (\mathsf{Sets},\times ,\text{pt}\webright ) \to \webleft (\mathsf{Sets}_{*},\wedge ,S^{0}\webright ), \]

being equipped with isomorphisms of pointed sets

\[ \begin{gathered} \webleft (-\webright )^{+,\times }_{X,Y} \colon X^{+}\wedge Y^{+} \xrightarrow {\cong }\webleft (X\times Y\webright )^{+},\\ \webleft (-\webright )^{+,\times }_{\mathbb {1}} \colon S^{0} \xrightarrow {\cong }\text{pt}^{+}, \end{gathered} \]

natural in $X,Y\in \text{Obj}\webleft (\mathsf{Sets}\webright )$.

Noticed something off, or have any comments? Feel free to reach out!

You can also use the contact form below: