Cocone (Category Theory)

In category theory, a cocone for a diagram $D:\mathcal{I}\Rightarrow \mathcal{C}$ is a $\mathcal{C}$ object, $d$ paired with a Natural Transformation $N:D\Rightarrow \Delta d$ where $\Delta d:\mathcal{I}\Rightarrow \mathcal{C}$ is the constant functor. Naturality tells us that for all $f:a\to b$ in $D$, the cocone commutes with $f$.

\usepackage{tikz-cd}
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\begin{tikzcd}
a \arrow[d, "\alpha_a"] \arrow[r, "f"] & b \arrow[d, "\alpha_b"] \\
d \arrow[r, "id_d"] & d
\end{tikzcd}
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