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Commit 455e92aa authored by Philip Kaluđerčić's avatar Philip Kaluđerčić :u7121:
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Mention the "respect system dynamics" phrase

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...@@ -10,11 +10,12 @@ ...@@ -10,11 +10,12 @@
\begin{definition}\label{def:fcoalgebra} \begin{definition}\label{def:fcoalgebra}
In a \de{category} \(\C\), given an \de{object} \(A \in \Ob{\C}\) In a \de{category} \(\C\), given an \de{object} \(A \in \Ob{\C}\)
and an \de{endofunctor} \(F : \map{\C}{\C}\) the pair and an \de{endofunctor} \(F : \map{\C}{\C}\) the pair
\(A, a : \map{A}{F(A)}\) is called a \emph{\fca}. A \fca-homomorphism \(A, a : \map{A}{F(A)}\) is called a \emph{\fca}. A
\(f : \map{(A, a)}{(B, b)}\) ensures \( f \circ a = b \circ F(f)\). \fca-homomorphism \(f : \map{(A, a)}{(B, b)}\) ensures
\fca{}s and \fca-homomorphisms constitute a separate \de{category} \( f \circ a = b \circ F(f)\). \fca{}s and \fca-homomorphisms
\(\Coalg{F}\) \refsk{fca-category}, which is \textbf{not} dual to (which respect the system dynamics) constitute a separate
\(\Alg{F}\), but to \(\Alg{\op{F}}\). \de{category} \(\Coalg{F}\) \refsk{fca-category}, which is
\textbf{not} dual to \(\Alg{F}\), but to \(\Alg{\op{F}}\).
Despite that qualification, results like \cref{lem:lambek} or Despite that qualification, results like \cref{lem:lambek} or
\cref{def:initial-fa-construction} can mostly be derived analogously. \cref{def:initial-fa-construction} can mostly be derived analogously.
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