\\(\def\cat#1{{\mathcal{#1}}}\\) \\(\def\comp#1{{\widehat{#1}}}\\) \\(\def\conj#1{{\check{#1}}}\\) \\(\def\id{{\mathrm{id}}}\\) \\(\def\true{{\mathrm{true}}}\\) \\(\def\false{{\mathrm{false}}}\\) \\(\def\Cat#1{{\textbf{#1}}}\\) \\(\def\BB{{\mathbb{B}}}\\) \\(\def\ZZ{{\mathbb{Z}}}\\) \\(\def\tn#1{{\text{#1}}}\\)
Consider the monoidal category \\((\Cat{Set},1,\times)\\), together with the diagram

![](https://cdn.rawgit.com/DavidRLambert/61cd3d226372556d99c1bd8631ff9833/raw/ca1d98ea6ce9b63ae1afb8c5d22d9c1d4194515a/20180814Diagram.svg)

Suppose that \\(A=B=C=D=F=G=\ZZ\\) and \\(E=\BB=\{\true,\false\}\\),
and suppose that \\(f_C(a)=|a|\\), \\(f_D(a)=a*5\\), \\(g_E(d,b)=d\leq b\\), \\(g_F(d,b)=d-b\\), and \\(h(c,e)=\tn{if }e\tn{ then }c\tn{ else }1-c\\).

1. What are \\(g_E(5,3)\\) and \\(g_F(5,3)\\)?
2. What are \\(g_E(3,5)\\) and \\(g_F(3,5)\\)?
3. What is \\(h(5,\true)\\)?
4. What is \\(h(-5,\true)\\)?
5. What is \\(h(-5,\false)\\)?

The whole diagram now defines a function \\(A\times B\to G\times F\\); call it \\(q\\).

6. What are \\(q_G(-2,3)\\) and \\(q_F(-2,3)\\)?
7. What are \\(q_G(2,3)\\) and \\(q_F(2,3)\\)?