Theorems · Theorem · category theory
CategoryTheory.Abelian.Ext.bilinearComp_apply_apply
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : CategoryTheory.HasExt C] (X Y Z : C) (a b c : ℕ) (h : a + b = c) (α : CategoryTheory.Abelian.Ext X Y a)
(β : CategoryTheory.Abelian.Ext Y Z b), ((CategoryTheory.Abelian.Ext.bilinearComp X Y Z a b c h) α) β = α.comp β h- Cited by
- 8 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- AddMonoidHomstatement · cited by 3,230
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.HasExtstatement and proof · cited by 218
- CategoryTheory.Abelian.Extstatement and proof · cited by 191
- CategoryTheory.Abelian.Ext.compstatement · cited by 80
- CategoryTheory.Abelian.Ext.bilinearCompstatement and proof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.postcomp_mk₀_injective_of_monoproof · cited by 1
- CategoryTheory.Abelian.Ext.postcomp_smul_id_eq_zero_of_mem_annihilatorproof · cited by 1
- CategoryTheory.Abelian.Ext.postcomp_smul_id_mono_iffproof · cited by 1
- CategoryTheory.Abelian.Ext.precomp_mk₀_injective_of_epiproof · cited by 1
- ModuleCat.projectiveDimension_quotSMulTop_eq_succ_of_isSMulRegularproof · cited by 1
- CategoryTheory.Functor.mapExt_bijective_of_preservesInjectiveObjectsproof · cited by 0
- CategoryTheory.Functor.mapExt_bijective_of_preservesProjectiveObjectsproof · cited by 0
- CategoryTheory.Sheaf.H.map_add_applyproof · cited by 0