diff --git a/src/content/1.5/Products and Coproducts.tex b/src/content/1.5/Products and Coproducts.tex index 70abab50..91a87ed5 100644 --- a/src/content/1.5/Products and Coproducts.tex +++ b/src/content/1.5/Products and Coproducts.tex @@ -296,14 +296,13 @@ \section{Products} But we haven't explored yet the other part of the universal construction: the ranking. We want to be able to compare two instances of our pattern. We want to compare one candidate object $c$ and its -two projections \emph{p} and \emph{q} with another candidate object -$c'$ and its two projections \emph{p'} and \emph{q'}. We would like +two projections $p$ and $q$ with another candidate object +$c'$ and its two projections $p'$ and $q'$. We would like to say that $c$ is ``better'' than $c'$ if there is a morphism $m$ from $c'$ to $c$ --- but that's too weak. We also want its projections to be ``better,'' or ``more universal,'' than the projections of $c'$. What it means is that the projections -\emph{p'} and \emph{q'} can be reconstructed from \emph{p} and \emph{q} -using $m$: +$p'$ and $q'$ can be reconstructed from $p$ and $q$ using $m$: \src{code/haskell/snippet12.hs} @@ -314,9 +313,9 @@ \section{Products} \noindent Another way of looking at these equations is that $m$ -\emph{factorizes} \emph{p'} and \emph{q'}. Just pretend that these +\emph{factorizes} $p'$ and $q'$. Just pretend that these equations are in natural numbers, and the dot is multiplication: -$m$ is a common factor shared by \emph{p'} and \emph{q'}. +$m$ is a common factor shared by $p'$ and $q'$. Just to build some intuitions, let me show you that the pair \code{(Int, Bool)} with the two canonical projections, \code{fst}