> This sort of leads me to wonder if we can generalize the above as a special case of two more general rules:

> 1. Is \$$\hat{F} \otimes \hat{G} = \widehat{F \times G}\$$?
> 2. Is \$$\check{F} \otimes \check{G} = \overline{F \times G}\$$?

> Moreover, thinking about Puzzle 207, I have been wondering:

> 3. Is \$$\hat{F} \hat{G} = \widehat{F \circ G}\$$?
> 4. Is \$$\check{F} \check{G} = \overline{F \circ G}\$$?

>I think the answer to those two questions is *yes* but I don't quite know...

I think the first one of those is certainly true @Matthew:

\$$(\hat{F} \otimes \hat{G})((x, x'), (y, y'))\$$

\$$= \hat{F}(x, y) \otimes \hat{G}(x', y')\$$

\$$= Y(Fx, y) \otimes Y'(Gx', y')\$$

\$$= (Y \times Y')((Fx, Gx'), (y, y'))\$$

\$$= (Y \times Y')((F \times G)(x, x'), (y, y'))\$$

\$$= (\widehat{F \times G})((x, x'), (y, y'))\$$