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Null maps, null types and null type families

Open fredrik-bakke opened this issue 1 year ago • 1 comments

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 A is a retract of B and S is a retract of T then diagonal-exponential A S is a retract of diagonal-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 of Y is orthogonal to the terminal projection of A
  • 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

fredrik-bakke avatar Mar 20 '24 16:03 fredrik-bakke

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.

fredrik-bakke avatar Apr 24 '24 17:04 fredrik-bakke