Generalized Reedy diagrams in tribes

Starting from a generalized Reedy category $R$ satisfying a simple condition, we construct an absolutely dense functor $\mathbf{D}_R \to R$ with domain a strict Reedy category. In the case of a generalized inverse category $R$, and given any tribe $\mathcal{T}$, we leverage this construction to provide a tribe structure on a subcategory of fibrant diagrams in $\mathcal{T}^R$.

💡 Research Summary

The paper addresses two intertwined problems at the interface of higher‑category theory and homotopy‑type‑theoretic structures. First, given a generalized Reedy category R that satisfies a modest “simple condition” (namely that every non‑identity morphism can be factored into a degree‑decreasing part followed by a degree‑increasing part), the authors construct a strict Reedy category (\mathbf{D}_R) together with a functor
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