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Where has this structure been observed?

This is an infinite commutative diagram on $M$ (viewed as a category with a single object $\bullet$). $\require{AMScd}$ \begin{CD} \vdots @. \vdots @. \vdots\\ @VVR_y(0,2)V @VVR_y(1,2)V @VVR_y(2,2)V\...
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