Item 1 (00T0) — 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.

Functoriality. The assignment $U\mapsto R_{!}\webleft (U\webright )$ defines a functor
\[ R_{!}\colon \webleft (\mathcal{P}\webleft (A\webright ),\subset \webright )\to \webleft (\mathcal{P}\webleft (B\webright ),\subset \webright ) \]

where
- Action on Objects. For each $U\in \mathcal{P}\webleft (A\webright )$, we have
  
  \[ \webleft [R_{!}\webright ]\webleft (U\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}R_{!}\webleft (U\webright ); \]
- Action on Morphisms. For each $U,V\in \mathcal{P}\webleft (A\webright )$:
  - If $U\subset V$, then $R_{!}\webleft (U\webright )\subset R_{!}\webleft (V\webright )$.

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

You can also use the contact form below: