Item 2 (00RD) — 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.

Adjointness. We have an adjunction
witnessed by a bijections of sets
\[ \textup{Hom}_{\mathcal{P}\webleft (A\webright )}\webleft (R_{*}\webleft (U\webright ),V\webright )\cong \textup{Hom}_{\mathcal{P}\webleft (A\webright )}\webleft (U,R_{-1}\webleft (V\webright )\webright ), \]

natural in $U\in \mathcal{P}\webleft (A\webright )$ and $V\in \mathcal{P}\webleft (B\webright )$, i.e. such that:
- The following conditions are equivalent:
  - We have $R_{*}\webleft (U\webright )\subset V$;
  - We have $U\subset R_{-1}\webleft (V\webright )$.

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

You can also use the contact form below: