Item 3 (007N) — 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.

Preservation of Colimits. We have an equality of sets
\[ f_{*}\webleft (\bigcup _{i\in I}U_{i}\webright )=\bigcup _{i\in I}f_{*}\webleft (U_{i}\webright ), \]

natural in $\webleft\{ U_{i}\webright\} _{i\in I}\in \mathcal{P}\webleft (A\webright )^{\times I}$. In particular, we have equalities

\[ \begin{gathered} f_{*}\webleft (U\webright )\cup f_{*}\webleft (V\webright ) = f_{*}\webleft (U\cup V\webright ),\\ f_{*}\webleft (\emptyset \webright ) = \emptyset , \end{gathered} \]

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

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

You can also use the contact form below: