Diagram

Let be a Category (almost always Small Category, often finite). A diagram of shape in is a functor . The Objects for are called vertices of , and the morphisms for are called edges of .

Example

If is the Category

\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
 \cdot \arrow[r] \arrow[d] \arrow[dr]
 & \cdot \arrow[d] \\
 \cdot\arrow[r]
 & \cdot
\end{tikzcd}
\end{document}

a diagram of shape is a commutative square.

If is

\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
 \cdot \arrow[r] \arrow[d] \arrow[dr,shift left] \arrow[dr, shift right]
 & \cdot \arrow[d] \\
 \cdot\arrow[r]
 & \cdot
\end{tikzcd}
\end{document}

a diagram of shape is a not-necessarily-commutative square.