diff --git a/README.md b/README.md index cb030ff..d784e35 100644 --- a/README.md +++ b/README.md @@ -33,8 +33,8 @@ feature-flags. Afterwards, type `nix flake show` in the root directory of the project to see all the available versions of this book. Then type `nix build .#` to -build the edition you want (Scala, OCaml, Reason and their printed -versions). For example, to build the Scala edition you'll have to type +build the edition you want (Scala, OCaml, Reason and their printed versions). +For example, to build the Scala edition you'll have to type `nix build .#ctfp-scala`. For Haskell (the original version) that is just `nix build .#ctfp`. diff --git a/src/content/3.14/lawvere-theories.tex b/src/content/3.14/lawvere-theories.tex index c1cc415..655d817 100644 --- a/src/content/3.14/lawvere-theories.tex +++ b/src/content/3.14/lawvere-theories.tex @@ -63,7 +63,7 @@ the roadmap: Lawvere theory $\cat{L}$: an object in the category $\cat{Law}$. \item Model $M$ of a Lawvere category: an object in the category\\ - $\cat{Mod}(\cat{Law}, \Set)$. + $\cat{Mod}(\cat{L}, \Set)$. \end{enumerate} \begin{figure}[H] @@ -352,7 +352,7 @@ $n$. We can implement $F$ as the representable functor: \[\cat{L}(n, -) \Colon \cat{L} \to \Set\] To show that it's indeed free, all we have to do is to prove that it's a left adjoint to the forgetful functor: -\[\cat{Mod}(\cat{L}(n, -), M) \cong \Set(n, U(M))\] +\[\cat{Mod}(\cat{L}, \Set)(\cat{L}(n, -), M) \cong \Set(n, U(M))\] Let's simplify the right hand side: \[\Set(n, U(M)) \cong \Set(n, M 1) \cong (M 1)^n \cong M n\] (I used the fact that a set of morphisms is isomorphic to the