Structures · Category theory
CategoryTheory.Limits.HasStrictInitialObjects
We say C has strict initial objects if every initial object is strict, i.e. given any morphism
f : A ⟶ I where I is initial, then f is an isomorphism.
Strictly speaking, this says that any initial object must be strict, rather than that strict
initial objects exist.
- Shape
- One type argument · adds out
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by1
Forgetful instances
Provided automatically by
Concrete types that are instances1
- AlgebraicGeometry.Scheme
How is a type an instance?
Loading the hierarchy index…
Assumed by36
- CategoryTheory.MorphismProperty.overEquivOfIsInitial
- CategoryTheory.overEquivOfIsInitial
- CategoryTheory.Limits.isInitialMul
- CategoryTheory.Limits.IsInitial.strict_hom_ext
- CategoryTheory.Limits.mulIsInitial
- CategoryTheory.Limits.mulInitial
- CategoryTheory.isVanKampenColimit_of_isEmpty
- CategoryTheory.Limits.IsInitial.isIso_to
- CategoryTheory.Limits.initialMul
- CategoryTheory.Limits.IsInitial.subsingleton_to
- CategoryTheory.Limits.HasStrictInitialObjects.out
- CategoryTheory.IsInitial.isVanKampenColimit
- CategoryTheory.Limits.initial.strict_hom_ext
- CategoryTheory.Limits.isInitialMul_hom
- CategoryTheory.GrothendieckTopology.preservesColimitsOfShape_yoneda_of_ofArrows_inj_mem
- CategoryTheory.MorphismProperty.overEquivOfIsInitial_functor
- CategoryTheory.Limits.initial_isIso_to
- CategoryTheory.overEquivOfIsInitial_unitIso
- CategoryTheory.MorphismProperty.overEquivOfIsInitial_inverse
- CategoryTheory.Limits.mulIsInitial_inv
- CategoryTheory.overEquivOfIsInitial_counitIso
- CategoryTheory.Limits.mulIsInitial_hom
- CategoryTheory.overEquivOfIsInitial_inverse
- CategoryTheory.Limits.initialMul_inv
- CategoryTheory.Limits.initial_mono_of_strict_initial_objects
- CategoryTheory.overEquivOfIsInitial_functor
- CategoryTheory.Limits.isInitialMul_inv
- CategoryTheory.Limits.mulInitial_hom
- CategoryTheory.MorphismProperty.overEquivOfIsInitial_counitIso
- CategoryTheory.Limits.initialMul_hom
- CategoryTheory.Limits.mulInitial_inv
- CategoryTheory.Limits.initial.subsingleton_to
- CategoryTheory.Limits.initial.strict_hom_ext_iff
- CategoryTheory.MorphismProperty.overEquivOfIsInitial_unitIso
- CategoryTheory.Limits.IsInitial.ofStrict
- CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfCommSq
Ancestors0
No ancestors.