diff --git a/thesis/1_CategoryTheory.tex b/thesis/1_CategoryTheory.tex index ebb773f..802deb0 100644 --- a/thesis/1_CategoryTheory.tex +++ b/thesis/1_CategoryTheory.tex @@ -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}