agda-unimath
agda-unimath copied to clipboard
Null maps, null types and null type families
Defines Y-null maps, Y-null types and Y-null type families, and establishes a few basic properties of these. Also formalizes the fiber condition for orthogonal maps. Part of #930. Depends on #1086.
- If
Ais a retract ofBandSis a retract ofTthendiagonal-exponential A Sis a retract ofdiagonal-exponential B T. - Null types
- Null types are closed under equivalences in the base and exponent
- Null types are closed under retracts in the base and exponent
- A type is
Y-null if and only if the terminal projection ofYis orthogonal to the terminal projection ofA
- Null families
- Null families are closed under equivalences in the family and exponent
- Null families are closed under retracts in the family and exponent
- Null maps, equivalence of
- Fiber condition
- Pullback condition
- Right orthogonal map to terminal projection condition
- Local at terminal projection condition
- Fiber condition for orthogonal maps
I think this PR is mostly ready for review now, so I've marked it as such. 😁 I might end up wanting to use some of this in #1118 soon.