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Leon Vatthauer 2024-01-21 17:26:55 +01:00
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slides/sections/01_abstracting.tex
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@ -177,7 +177,7 @@ The following is an adaptation of Ad\'amek, Milius and Velebil's \textit{complet
\item \textbf{Fixpoint}: $f^\dagger = [ \eta , f^\dagger ]^* \circ f$ \item \textbf{Fixpoint}: $f^\dagger = [ \eta , f^\dagger ]^* \circ f$
\\for $f : X \rightarrow T(Y + X)$ \\for $f : X \rightarrow T(Y + X)$
\item \textbf{Uniformity}: $f \circ h = T(id + h) \circ g \Rightarrow f^\dagger \circ h = g^\dagger$ \item \textbf{Uniformity}: $f \circ h = T(id + h) \circ g \Rightarrow f^\dagger \circ h = g^\dagger$
\\for $f : X \rightarrow T(Y + X) , g : Z \rightarrow T(Y + Z)$ \\for $f : X \rightarrow T(Y + X) , g : Z \rightarrow T(Y + Z), h : Z \rightarrow X$
\item \textbf{Naturality}: $g^* \circ f^\dagger = ([ (T inl) \circ g , \eta \circ inr ]^* \circ f )^\dagger$ \item \textbf{Naturality}: $g^* \circ f^\dagger = ([ (T inl) \circ g , \eta \circ inr ]^* \circ f )^\dagger$
\\for $f : X \rightarrow T(Y + X), g : Y \rightarrow TZ$ \\for $f : X \rightarrow T(Y + X), g : Y \rightarrow TZ$
\item \textbf{Codiagonal}: $f^{\dagger\dagger} = (T[id , inr ] \circ f)^\dagger$ \item \textbf{Codiagonal}: $f^{\dagger\dagger} = (T[id , inr ] \circ f)^\dagger$