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