  This paper develops a theory of colimit sketches "with constructions" in
higher category theory, formalising the input to the ubiquitous procedure of
adjoining specified "constructible" colimits to a category such that specified
"relation" colimits are enforced (or preserved). From a more technical
standpoint, sketches are a way to describe dense functors using techniques from
the homotopy theory of diagrams.
  We establish basic properties of diagrams in an infinity-category C as a
model for presheaves on C and Bousfield localisations thereof, discuss
extensions of functors and adjunctions, and equivalences of sets of diagrams.
We introduce categories of presheaves which are "constructible in one step" by
a set of diagrams and explore, via well-known examples, when constructible
cocompletion is idempotent, i.e. when any iterated construction can be
completed in one step.
