Displayed Category of Functor Dialgebras

Let $F,G:\mathcal{C}\to\mathcal{D}$ be a pair of Functors. The displayed category of $F,G$-dialgebras is the Displayed Category where

• Objects over $X$ are Functor Dialgebras; EG: maps $F(X)\to G(X)$
• Morphisms over $f:X\to Y$ between functor dialgebras $\alpha:F(X)\to G(X)$, $\beta:F(Y)\to G(Y)$ are proofs that $G(f)\circ\alpha=\beta\circ F(f)$.

Properties

• The displayed category of functor dialgebras is a Pullback of the displayed comma category $F/G\rightarrowtriangle\mathcal{C}\times\mathcal{C}$ along the diagonal functor $\Delta:\mathcal{C}\to\mathcal{C}\times\mathcal{C}$.