Structures · Category theory
CategoryTheory.HasProjectiveResolutions
You will rarely use this typeclass directly: it is implied by the combination
[EnoughProjectives C] and [Abelian C].
By itself it's enough to set up the basic theory of derived functors.
- Shape
- One type argument · adds out
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Forgetful instances
Every CategoryTheory.HasProjectiveResolutions is also a
Concrete types that are instances0
No instance on a concrete type; it is reached through other classes.
How is a type an instance?
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Assumed by57
- CategoryTheory.Functor.leftDerived
- CategoryTheory.Functor.leftDerivedToHomotopyCategory
- CategoryTheory.Functor.leftDerivedZeroIsoSelf
- CategoryTheory.Functor.fromLeftDerivedZero
- CategoryTheory.NatTrans.leftDerived
- CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj
- CategoryTheory.ProjectiveResolution.isoLeftDerivedObj
- CategoryTheory.projectiveResolutions
- CategoryTheory.ProjectiveResolution.iso
- CategoryTheory.NatTrans.leftDerivedToHomotopyCategory
- CategoryTheory.Tor'
- CategoryTheory.Tor
- CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality
- CategoryTheory.Functor.isZero_leftDerived_obj_projective_succ
- CategoryTheory.ProjectiveResolution.iso_inv_naturality
- CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality
- CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp
- CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality
- CategoryTheory.NatTrans.leftDerived_comp
- CategoryTheory.ProjectiveResolution.iso_hom_naturality
- CategoryTheory.ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq
- CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality
- CategoryTheory.ProjectiveResolution.iso_inv_naturality_assoc
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id
- CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality_assoc
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_app
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id
- CategoryTheory.Functor.leftDerived_map_eq
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id_assoc
- CategoryTheory.ProjectiveResolution.fromLeftDerivedZero_eq
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc
- CategoryTheory.ProjectiveResolution.leftDerived_app_eq
- CategoryTheory.Tor'_obj_map
- CategoryTheory.Functor.leftDerived.congr_simp
- CategoryTheory.ProjectiveResolution.iso_hom_naturality_assoc
- CategoryTheory.Tor'_map_app
- CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_inv_naturality_assoc
- CategoryTheory.isZero_Tor'_succ_of_projective
- CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom
- CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp_assoc
- CategoryTheory.NatTrans.leftDerived_comp_assoc
- CategoryTheory.Tor_map
- CategoryTheory.NatTrans.leftDerived_id
- CategoryTheory.Functor.leftDerivedZeroIsoSelf.congr_simp
- CategoryTheory.instIsIsoFunctorFromLeftDerivedZero
- CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality_assoc
- CategoryTheory.isZero_Tor_succ_of_projective
- CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality_assoc
- CategoryTheory.Tor'_obj_obj