From 2915987d9209b81c0b5dab1ea1a1500e9b5540cf Mon Sep 17 00:00:00 2001 From: Nelson Niu Date: Mon, 15 Jul 2024 11:30:57 -0700 Subject: [PATCH] polish co & suppliers --- P1-Polynomials.tex | 14 +++++++++----- 1 file changed, 9 insertions(+), 5 deletions(-) diff --git a/P1-Polynomials.tex b/P1-Polynomials.tex index 59aed2f..d486e3b 100644 --- a/P1-Polynomials.tex +++ b/P1-Polynomials.tex @@ -7128,13 +7128,13 @@ \subsection{More examples of general interaction} \end{example} \begin{example}\label{ex.supplier_change}\index{interaction!supplier change} -Consider the case of a company that may change its supplier based on its internal state. The company returns two possible positions, corresponding to who it wants to receive widgets $W$ from: +Consider the case of a company that may change its supplier based on its internal state. The company returns two possible positions, corresponding to whether it wants to receive gizmos in $G$ from the first supplier or widgets in $W$ from the second: \[ \begin{tikzpicture}[oriented WD, every node/.style={fill=blue!10}] \node[bb={0}{1}] (s1) {Supplier 1}; \node[bb={0}{1}, below=of s1] (s2) {Supplier 2}; \node[bb={1}{0}, right=0.5 of s1] (c) {Company}; - \draw (s1_out1) to node[above, fill=none, font=\tiny] {$W$} (c_in1); + \draw (s1_out1) to node[above, fill=none, font=\tiny] {$G$} (c_in1); \draw (s2_out1) to +(5pt,0) node[fill=none] {$\bullet$}; \begin{scope}[xshift=3.5in] \node[bb={0}{1}] (s1') {Supplier 1}; @@ -7147,9 +7147,13 @@ \subsection{More examples of general interaction} {Change\\supplier!}; \end{tikzpicture} \] -So the company has interface $\2\yon^W$, and each supplier has interface $W\yon$. -Then a section for the company and the suppliers is just a lens $\2\yon^W\otimes W\yon\otimes W\yon\to\yon$, corresponding to a function $\2W^\2\to W$ given by evaluation. -In other words, the company's position determines its supplier. +So the company has interface $\{1\}\yon^G+\{2\}\yon^W$, the first supplier has interface $G\yon$, and the second supplier has interface $W\yon$. +Then a section for the company and the suppliers is a lens +\[ + \left(\{1\}\yon^G+\{2\}\yon^W\right)\otimes G\yon\otimes W\yon\to\yon, +\] +corresponding to a pair of functions $\{1\}\times GW\iso GW\to G$ and $\{2\}\times GW\iso GW\to W$ given by canonical projections. +In other words, the company's position determines its supplier and what it receives. \end{example} \begin{example}\label{ex.assemble_machine}\index{interaction!assembling}