Sketches
Ehresmann's concept of sketch is very widely generalized here. The basis for it is an object \({\mathcal C}\) in some 3-dimensional categorical setting (such as locally finitely presentable 2-categories) and a monad \(T\) on \({\mathcal C}\). They take, as diagram types, arrows \(c,d:{\mathcal I}\to {\mathcal C}\) with a factorization of the unit of \(T\) into the composite of 2-cells \(j:c\to d\) and \(k:d\to Tc\). A sketch, relative to \(u:{\mathcal I}\to {\mathcal U}\) for this diagram type, consists of an arrow \(x:{\mathcal U}\to{\mathcal C}\) and a 2-cell \(p:d\to xu\). these sketches are modelled (strictly and strongly) in \(T\)-algebras \(a:{\mathcal U}\to{\mathcal C}\).
scientific article; zbMATH DE number 1384152