Structures · Category theory
CategoryTheory.Limits.HasZeroMorphisms
A category "has zero morphisms" if there is a designated "zero morphism" in each morphism space, and compositions of zero morphisms with anything give the zero morphism.
- Shape
- One type argument · adds zero, comp_zero, zero_comp
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by1
Concrete types that are instances16
- CategoryTheory.Functor
- CategoryTheory.Discrete
- CategoryTheory.Grp
- HomologicalComplex
- Action
- CategoryTheory.Mon
- CategoryTheory.ObjectProperty.FullSubcategory
- CategoryTheory.GradedObject
- CategoryTheory.AddGrp
- CategoryTheory.AddMon
- CategoryTheory.ShortComplex
- SemimoduleCat
- CategoryTheory.DifferentialObject
- SemiNormedGrp
- SemiNormedGrp₁
- Opposite
How is a type an instance?
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Assumed by4,633
- HomologicalComplex.X
- CategoryTheory.ShortComplex.X₂
- CochainComplex
- CategoryTheory.ShortComplex.X₁
- CategoryTheory.ShortComplex.X₃
- HomologicalComplex.Hom.f
- CategoryTheory.ShortComplex.g
- CategoryTheory.ShortComplex.f
- HomologicalComplex.d
- CategoryTheory.Limits.comp_zero
- ChainComplex
- HomologicalComplex.HasHomology
- CategoryTheory.Limits.zero_comp
- CategoryTheory.Limits.biprod
- CategoryTheory.Limits.kernel
- CategoryTheory.ShortComplex.Hom.τ₂
- CategoryTheory.ShortComplex.LeftHomologyData.H
- CategoryTheory.ShortComplex.LeftHomologyData.K
- CategoryTheory.Limits.cokernel
- CategoryTheory.ShortComplex.cycles
- CategoryTheory.ShortComplex.homology
- CategoryTheory.Limits.kernel.ι
- HomologicalComplex.homology
- HomologicalComplex.sc
- CategoryTheory.ShortComplex.Hom.τ₃
- CategoryTheory.Limits.cokernel.π
- CategoryTheory.ShortComplex.Hom.τ₁
- CategoryTheory.ShortComplex.opcycles
- CategoryTheory.ShortComplex.map
- CategoryTheory.Limits.biproduct
- CategoryTheory.Limits.HasKernel
- HomologicalComplex.cycles
- CategoryTheory.ShortComplex.RightHomologyData.Q
- CategoryTheory.ShortComplex.RightHomologyData.H
- HomologicalComplex.opcycles
- HomologicalComplex₂
- CategoryTheory.Functor.mapHomologicalComplex
- CategoryTheory.ShortComplex.LeftHomologyData.i
- CategoryTheory.Limits.biprod.snd
- CategoryTheory.Limits.HasCokernel
- CategoryTheory.ShortComplex.HomologyData.left
- CategoryTheory.Limits.biprod.inl
- CategoryTheory.Limits.biprod.fst
- HomologicalComplex.extend
- HomologicalComplex.sc'
- HomologicalComplex.single
- HomologicalComplex.mapBifunctor
- CategoryTheory.Limits.biprod.inr
- CategoryTheory.Limits.CokernelCofork
- CategoryTheory.Limits.KernelFork
Ancestors0
No ancestors.