  Colimits are a fundamental construction in category theory. They provide a
way to construct new objects by gluing together existing objects that are
related in some way. We introduce a complementary notion of anticolimits, which
provide a way to decompose an object into a colimit of other objects. While
anticolimits are not unique in general, we establish that in the presence of
pullbacks, there is a "canonical" anticolimit which characterises the existence
of other anticolimits. We also provide convenient techniques for computing
anticolimits, by changing either the shape or ambient category.
  The main motivation for this work is the development of a new method, known
as anticontraction, for constructing homotopies in the proof assistant
homotopy.io for finitely presented $n$-categories. Anticontraction complements
the existing contraction method and facilitates the construction of homotopies
increasing the complexity of a term, enhancing the usability of the proof
assistant. For example, it simplifies the naturality move and third
Reidemeister move.
