If
is a commutative diagram in a category , then a filler (synonyms: diagonal fill-in, lift) is:
In certain contexts, the problem of whether there exists a filler in this sense is called a lifting problem.
If is uniquely determined (in an appropriate sense), then is said to be orthogonal to : see orthogonality.
The concept of filler plays an important role in homotopy theory; see for example model category.
The term is used in the context of horns in simplicial sets and related structures. The term makes it possible to summarize the definition of a Kan complex in one sentence: a Kan complex is a simplicial set in which every horn has a filler.
Of course this is a special case of the preceding notion of filler: a horn filler for a horn in a simplicial set is a diagonal fill-in of a commutative square
going from to .
Last revised on July 19, 2017 at 18:20:44. See the history of this page for a list of all contributions to it.