  In a type-theoretic fibration category in the sense of Shulman (representing
a dependent type theory with at least 1, Sigma, Pi, and identity types), we
define the type of constant functions from A to B. This involves an infinite
tower of coherence conditions, and we therefore need the category to have Reedy
limits of diagrams over omega. Our main result is that, if the category further
has propositional truncations and satisfies function extensionality, the type
of constant function is equivalent to the type ||A|| -> B.
  If B is an n-type for a given finite n, the tower of coherence conditions
becomes finite and the requirement of nontrivial Reedy limits vanishes. The
whole construction can then be carried out in Homotopy Type Theory and
generalises the universal property of the truncation. This provides a way to
define functions ||A|| -> B if B is not known to be propositional, and it
streamlines the common approach of finding a proposition Q with A -> Q and Q ->
B.
