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CT: It was a bit more subtle than I remembered

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Joshua Moerman 2013-05-28 15:42:55 +02:00
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thesis/1_CategoryTheory.tex
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@ -102,8 +102,9 @@ With the notion of isomorphisms between functors we can weaken this, and only re
\subsection{Adjunctions}
\begin{definition}
An \emph{adjunction} between two categories $\cat{C}$ and $\cat{D}$ consists of two functors $F:\cat{C} \to \cat{D}$ and $G: \cat{D} \to \cat{C}$ such that there are natural transformations:
$$ FG \to \id_\cat{D} \text{ and } \id_\cat{C} \to GF. $$
An \emph{adjunction} between two categories $\cat{C}$ and $\cat{D}$ consists of two functors $F:\cat{C} \to \cat{D}$, $G: \cat{D} \to \cat{C}$ and two natural transformations:
$$ FG \to \id_\cat{D} \text{ and } \id_\cat{C} \to GF, $$
such that \todo{CT: adjunction}.
$F$ is called the left-adjoint and $G$ the right-adjoint.
\end{definition}