Showing changes from revision #6 to #7:
Added | Removed | Changed
Given a natural number and types and , a function is a -monic function if for all terms the fiber of over has an homotopy level of .
A equivalence is a -monic function. -monic functions are typically just called monic functions or inclusions.
The type of all -monic functions with domain and codomain is defined as
For Given every types natural number , and , has a homotopy level of . is called asubtype of , and is called a supertype of , if is inhabited. We define the proposition of subtype inclusion as
In particular, the type of all monic functions with domain and codomain , defined as
where is the propositional truncation of . If and are sets, then is a subset of and is a superset of .
is The a type of all subtypes ofproposition . in a universe is defined as 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 .