Item 5 (00SJ) — 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 Strict Monoidality With Respect to Unions. The direct image function of Item 1 has a symmetric strict monoidal structure
\[ \webleft (R^{-1},R^{-1,\otimes },R^{-1,\otimes }_{\mathbb {1}}\webright ) \colon \webleft (\mathcal{P}\webleft (A\webright ),\cup ,\text{Ø}\webright ) \to \webleft (\mathcal{P}\webleft (B\webright ),\cup ,\text{Ø}\webright ), \]

being equipped with equalities

\[ \begin{gathered} R^{-1,\otimes }_{U,V} \colon R^{-1}\webleft (U\webright )\cup R^{-1}\webleft (V\webright ) \mathbin {\overset {=}{\rightarrow }}R^{-1}\webleft (U\cup V\webright ),\\ R^{-1,\otimes }_{\mathbb {1}} \colon \text{Ø}\mathbin {\overset {=}{\rightarrow }}\text{Ø}, \end{gathered} \]

natural in $U,V\in \mathcal{P}\webleft (B\webright )$.

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

You can also use the contact form below: