For a suitable collection D of small categories, we define the D-accessible categories, generalizing the λ-accessible categories of Lair, Makkai, and Paré; here the λ-accessible categories are seen as the D-accessible categories where D consists of the λ-small categories. A small category C is called D-filtered when C-colimits commute with D-limits in the category of sets. An object of a catego...

We previously defined collagories essentially as “distributive allegories without zero morphisms”. Collagories are sufficient for accommodating the relation-algebraic approach to graph transformation, and closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. Heindel and Sobociński have recently characterised the Van-Kampen colimits use...

We give a precise characterization for when the models of the tensor product of sketches are structurally isomorphic to the models of either sketch in the models of the other. For each base category K call the just mentioned property (sketch) K-multilinearity. Say that two sketches are K-compatible with respect to base category K just in case in each K-model, the limits for each limit specifica...

The main aim of this paper is to obtain compositive cone factorizations from non-compositive ones by itereration. This is possible if and only if certain colimits of (possibly large) chains exist. In particular, we show that (strong-epi, mono) factorizations of cones exist if and only if joint coequalizers and colimits of chains of regular epimorphisms exist.