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Given a natural number , a function is a -monic function if for all terms the homotopy fiber of a function over has an homotopy level of .
A homotopy equivalence is a -monic function. -monic functions are typically just called monic functions . functions.
The type of all -monic functions with domain and codomain is defined as
For every natural number , has a homotopy level of .
In particular, the type of all monic functions with domain and codomain , defined as
is a proposition. is called a subtype of , and is called a supertype of . If and are sets, then is a subset of and is a superset of .