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Author SHA1 Message Date
Sergei Winitzki
065a6dd76b
Merge 42a1a120b0 into 1bd3e36e5a 2024-11-20 19:36:10 +00:00
EFanZh
1bd3e36e5a
Use consistent epsilon symbol (#335) 2024-10-20 16:27:37 +02:00
kkinugasa
d13765c717
fix typo in 3.14 (#340)
* fix typo in 3.14

* run prettier
2024-10-08 11:11:28 +02:00
Dan Shearer
8765d97d13
Correct the build command for Haskell (#339) 2024-09-25 15:21:11 +02:00
dependabot[bot]
f6b98020e9
Bump actions/download-artifact from 2 to 4.1.7 in /.github/workflows (#338)
Bumps [actions/download-artifact](https://github.com/actions/download-artifact) from 2 to 4.1.7.
- [Release notes](https://github.com/actions/download-artifact/releases)
- [Commits](https://github.com/actions/download-artifact/compare/v2...v4.1.7)

---
updated-dependencies:
- dependency-name: actions/download-artifact
  dependency-type: direct:production
...

Signed-off-by: dependabot[bot] <support@github.com>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>
2024-09-04 04:55:51 +02:00
Kazufumi Okuda
c46c3669d4
fix(Section 3.11): typo (A -> Set) (#336) 2024-06-20 15:06:14 +02:00
6 changed files with 13 additions and 12 deletions

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@ -80,7 +80,7 @@ jobs:
steps:
- name: Download build assets (${{ matrix.packages }}.pdf)
uses: actions/download-artifact@v2
uses: actions/download-artifact@v4.1.7
with:
name: ctfp
path: ctfp

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@ -33,9 +33,10 @@ 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 .#<edition>` to
build the edition you want (Haskell, Scala, OCaml, Reason and their printed
versions). For example, to build the Scala edition you'll have to type
`nix build .#ctfp-scala`.
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`.
Upon successful compilation, the PDF file will be placed in the `result`
directory.

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@ -336,13 +336,13 @@ the end:
We can use the product-exponential adjunction:
\[\int_a \int_i \Set(\cat{A}(K i, a),\ (F' a)^{D i})\]
The exponential is isomorphic to the corresponding hom-set:
\[\int_a \int_i \Set(\cat{A}(K i, a),\ \cat{A}(D i, F' a))\]
\[\int_a \int_i \Set(\cat{A}(K i, a),\ \Set(D i, F' a))\]
There is a theorem called the Fubini theorem that allows us to swap the
two ends:
\[\int_i \int_a \Set(\cat{A}(K i, a),\ A(D i, F' a))\]
\[\int_i \int_a \Set(\cat{A}(K i, a),\ \Set(D i, F' a))\]
The inner end represents the set of natural transformations between two
functors, so we can use the Yoneda lemma:
\[\int_i \cat{A}(D i, F' (K i))\]
\[\int_i \Set(D i, F' (K i))\]
This is indeed the set of natural transformations that forms the right
hand side of the adjunction we set out to prove:
\[[\cat{I}, \Set](D, F' \circ K)\]

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@ -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

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@ -157,7 +157,7 @@ diagrams commute:
\centering
\begin{tikzcd}[column sep=large, row sep=large]
L \arrow[rd, equal] \arrow[r, "L \circ \eta"]
& L \circ R \circ L \arrow[d, "\epsilon \circ L"] \\
& L \circ R \circ L \arrow[d, "\varepsilon \circ L"] \\
& L
\end{tikzcd}
\end{subfigure}%
@ -166,7 +166,7 @@ diagrams commute:
\centering
\begin{tikzcd}[column sep=large, row sep=large]
R \arrow[rd, equal] \arrow[r, "\eta \circ R"]
& R \circ L \circ R \arrow[d, "R \circ \epsilon"] \\
& R \circ L \circ R \arrow[d, "R \circ \varepsilon"] \\
& R
\end{tikzcd}
\end{subfigure}

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@ -330,7 +330,7 @@ with a comonad. They make the following diagrams commute:
\centering
\begin{tikzcd}[column sep=large, row sep=large]
a \arrow[rd, equal]
& Wa \arrow[l, "\epsilon_a"'] \\
& Wa \arrow[l, "\varepsilon_a"'] \\
& a \arrow[u, "\mathit{coa}"']
\end{tikzcd}
\end{subfigure}%