Item 1 (007D) — 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.

Universal Property. The pair $\webleft (\mathcal{P}\webleft (X\webright ),\chi _{\webleft (-\webright )}\webright )$ consisting of
- The powerset $\mathcal{P}\webleft (X\webright )$ of $X$;
- The characteristic embedding $\chi _{\webleft (-\webright )}\colon X\hookrightarrow \mathcal{P}\webleft (X\webright )$ of $X$ into $\mathcal{P}\webleft (X\webright )$;
satisfies the following universal property:
- Given another pair $\webleft (Y,f\webright )$ consisting of
  - A cocomplete poset $\webleft (Y,\preceq \webright )$;
  - A function $f\colon X\to Y$;
  there exists a unique cocontinuous morphism of posets
  
  \[ \webleft (\mathcal{P}\webleft (X\webright ),\subset \webright )\overset {\exists !}{\to }\webleft (Y,\preceq \webright ) \]
  
  making the diagram
  
  commute.

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

You can also use the contact form below: