Generalized inverse diagrams in tribes

Abstract

Starting from a generalized direct category $R$, we construct an absolutely dense functor ${\mathbf{D}}_r\to R$ with domain a strict direct category. Given any tribe $\mathcal{T}$, we leverage this construction to provide a tribe structure on a subcategory of fibrant diagrams in ${\mathcal{T}}^{R^{op}}$, assuming some finiteness condition on $R$.

13 pages, comments welcome! v2: restricted to the settings of inverse diagrams