Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Fix typesetting issues in Chapters 25 and 26. #159

Merged
merged 2 commits into from
Nov 7, 2018
Merged
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion src/content/3.10/Ends and Coends.tex
Original file line number Diff line number Diff line change
@@ -117,7 +117,7 @@ \section{Ends}
functions mapping the apex to the sets in the base. You may think of
this family as one polymorphic function --- a function that's
polymorphic in its return type:
\[\alpha \Colon \forall a\ .\ apex -> p\ a\ a\]
\[\alpha \Colon \forall a\ .\ apex \to p\ a\ a\]
Unlike in cones, within a wedge we don't have any functions that would
connect vertices of the base. However, as we've seen earlier, given any
morphism $f \Colon a \to b$ in $\cat{C}$, we can connect both
8 changes: 4 additions & 4 deletions src/content/3.9/Algebras for Monads.tex
Original file line number Diff line number Diff line change
@@ -119,7 +119,7 @@ \section{T-algebras}
free functor.

The left adjoint to $U^T$ is called $F^T$. It maps an object
$A$ in $\cat{C}$ to a free algebra in $\cat{C}^T$. The carrier
$a$ in $\cat{C}$ to a free algebra in $\cat{C}^T$. The carrier
of this free algebra is $T\ a$. Its evaluator is a morphism from
$T\ (T\ a)$ back to $T\ a$. Since $T$ is a monad,
we can use the monadic $\mu_a$ (\code{join} in Haskell) as the
@@ -247,8 +247,8 @@ \section{The Kleisli Category}

We've seen the Kleisli category before. It's a category constructed from
another category $\cat{C}$ and a monad $T$. We'll call this
category $\cat{C}^T$. The objects in the Kleisli category
$\cat{C}^T$ are the objects of $\cat{C}$, but the morphisms
category $\cat{C}_T$. The objects in the Kleisli category
$\cat{C}_T$ are the objects of $\cat{C}$, but the morphisms
are different. A morphism $f_{\cat{K}}$ from $a$ to $b$ in
the Kleisli category corresponds to a morphism $f$ from
$a$ to $T\ b$ in the original category. We call this
@@ -292,7 +292,7 @@ \section{The Kleisli Category}
back to $\cat{C}$. It takes an object $a$ from the Kleisli
category and maps it to an object $T\ a$ in $\cat{C}$. Its action
on a morphism $f_{\cat{K}}$ corresponding to a Kleisli arrow:
\[f \Colon a -> T\ b\]
\[f \Colon a \to T\ b\]
is a morphism in $\cat{C}$:
\[T\ a \to T\ b\]
given by first lifting $f$ and then applying $\mu$: