Structures · Category theory
CategoryTheory.ObjectProperty.IsSerreClass
A Serre class in an abelian category consists of a predicate which holds for the zero object and is closed under subobjects, quotients, extensions.
- Shape
- One type argument
Extends4
Extended by0
Nothing extends this class yet.
Concrete types that are instances1
- AddCommGrpCat
How is a type an instance?
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Assumed by89
- CategoryTheory.ObjectProperty.isoModSerre
- CategoryTheory.ObjectProperty.epiModSerre
- CategoryTheory.ObjectProperty.monoModSerre
- CategoryTheory.ObjectProperty.SerreClassLocalization.abelian
- CategoryTheory.ObjectProperty.SerreClassLocalization.map_eq_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.epi_map_iff
- CategoryTheory.ObjectProperty.epiModSerre_of_epi
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_map_iff
- CategoryTheory.ObjectProperty.monoModSerre_of_mono
- CategoryTheory.ObjectProperty.isoModSerre_iff_of_epi
- CategoryTheory.ObjectProperty.isoModSerre_iff_of_mono
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernel
- CategoryTheory.ObjectProperty.isoModSerre_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernel
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesEpimorphisms
- CategoryTheory.ObjectProperty.exists_epiModSerre_comp_eq_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.whiskeringLeft
- CategoryTheory.ObjectProperty.exists_comp_monoModSerre_eq_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.map_comp_eq_zero_iff_of_epi_mono
- CategoryTheory.ObjectProperty.exists_isoModSerre_comp_eq_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesMonomorphisms
- CategoryTheory.ObjectProperty.exists_comp_isoModSerre_eq_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_map_tfae
- CategoryTheory.ObjectProperty.epiModSerre.isoModSerre_image_ι
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasKernels
- CategoryTheory.ObjectProperty.SerreClassLocalization.isIso_map_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasCokernels
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteLimits_comp_iff
- CategoryTheory.ObjectProperty.isoModSerre_isInvertedBy_iff
- CategoryTheory.ObjectProperty.le_kernel_of_isoModSerre_isInvertedBy
- CategoryTheory.ObjectProperty.monomorphisms_le_monoModSerre
- CategoryTheory.ObjectProperty.SerreClassLocalization.epi_iff
- CategoryTheory.ObjectProperty.epimorphisms_le_epiModSerre
- CategoryTheory.ObjectProperty.isomorphisms_le_isoModSerre
- CategoryTheory.ObjectProperty.monoModSerre_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteColimits_comp_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteColimits
- CategoryTheory.ObjectProperty.SerreClassLocalization.exactFunctor_comp_iff
- CategoryTheory.ObjectProperty.epiModSerre_zero_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_iff
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteLimits
- CategoryTheory.ObjectProperty.SerreClassLocalization.epi_map_tfae
- CategoryTheory.ObjectProperty.monoModSerre.isoModSerre_factorThruImage
- CategoryTheory.ObjectProperty.instIsStableUnderCobaseChangeMonoModSerre
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasFiniteProducts
- CategoryTheory.ObjectProperty.instIsStableUnderRetractsEpiModSerre
- CategoryTheory.ObjectProperty.SerreClassLocalization.isNormalMonoCategory
- CategoryTheory.ObjectProperty.isoModSerre_of_isIso
- CategoryTheory.ObjectProperty.instIsStableUnderBaseChangeIsoModSerre
- CategoryTheory.ObjectProperty.isoModSerre_zero_iff