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Fix typos (#328)
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* typo in 1.8/functoriality.tex line 30

fix #233

* Typo in Preface

fix #265

* Replace ... with \ldots{}
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ktgw0316 authored Jan 28, 2024
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2 changes: 1 addition & 1 deletion src/content/0.0/preface.tex
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Expand Up @@ -40,7 +40,7 @@
definition of the category itself. And I will argue strongly that
composition is the essence of programming. We've been composing things
forever, long before some great engineer came up with the idea of a
subroutine. Some time ago the principles of structural programming
subroutine. Some time ago the principles of structured programming
revolutionized programming because they made blocks of code composable.
Then came object oriented programming, which is all about composing
objects. Functional programming is not only about composing functions
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2 changes: 1 addition & 1 deletion src/content/1.8/functoriality.tex
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Expand Up @@ -27,7 +27,7 @@ \section{Bifunctors}
morphisms, one from $\cat{C}$ and one from $\cat{D}$, to a morphism in $\cat{E}$.

Again, a pair of morphisms is just a single morphism in the product
category $\cat{C}\times{}\cat{D}$ to $\cat{E}$. We define a morphism in a Cartesian product of categories
category $\cat{C}\times{}\cat{D}$. We define a morphism in a Cartesian product of categories
as a pair of morphisms which goes from one pair of objects to another
pair of objects. These pairs of morphisms can be composed in the obvious
way:
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4 changes: 2 additions & 2 deletions src/content/3.14/lawvere-theories.tex
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Expand Up @@ -425,7 +425,7 @@ \section{Monads as Coends}
$a$, namely (notice the direction):
\[a^n \to a^m\]
The lifting simply selects $m$ elements from a tuple of $n$ elements\\
$(a_1, a_2,...a_n)$ (possibly with repetitions).
$(a_1, a_2, \ldots{}, a_n)$ (possibly with repetitions).

\begin{figure}[H]
\centering
Expand All @@ -441,7 +441,7 @@ \section{Monads as Coends}
Or let's take $f \Colon m \to 1$ --- a constant
function that maps all $m$ elements to one. Its lifting is a function that
takes a single element of $a$ and duplicates it $m$ times:
\[\lambda{}x \to (\underbrace{x, x,\ ...\ , x}_{m})\]
\[\lambda{}x \to (\underbrace{x, x, \ldots{}, x}_{m})\]
You might notice that it's not immediately obvious that the profunctor
in question is covariant in the second argument. The hom-functor
$\cat{L}(m, 1)$ is actually contravariant in $m$. However, we
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