SCT.VolumeI.Chapter02.Section01.IntervalEndpoints

Complete compiler-highlighted source. Follow a symbol to its declaration.

# Initial and terminal endpoints

`axiom:Initial_Terminal_Objects_Interval` says precisely that the two slice
projections defining initiality and terminality are equivalences. The
remaining interval operations will be constructed from these fields.

```agda
{-# OPTIONS --safe --without-K #-}
open import Agda.Primitive using (Level)
open import SCT.VolumeI.Chapter01.Theory using (Theory)
import SCT.VolumeI.Chapter01.Section04.MappingAnimae as Mapping
import SCT.VolumeI.Chapter01.Section07.FunctorCategories as Categories
import SCT.VolumeI.Chapter01.Section06.PullbackLaws as Laws
import SCT.VolumeI.Chapter02.Section01.WalkingMorphism as Walking

module SCT.VolumeI.Chapter02.Section01.IntervalEndpoints
  {c m a : Level} (𝒯 : Theory c m a) (M : Mapping.MappingAnimae 𝒯)
  (ℱ : Categories.FunctorCategories 𝒯 M) (P : Laws.PullbackStructure 𝒯)
  (I : Walking.WalkingMorphism 𝒯) where

open import SCT.VolumeI.Chapter02.Section01.HomAndSlices 𝒯 M ℱ P I

record IntervalEndpoints : Set m where
  field
    zero-isInitial : IsInitial zero
    one-isTerminal : IsTerminal one
```