Theorems · Theorem · category theory
CategoryTheory.ShiftedHom.comp.congr_simp
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {M : Type u_4} [inst_1 : AddMonoid M]
[inst_2 : CategoryTheory.HasShift C M] {X Y Z : C} {a b c : M} (f f_1 : CategoryTheory.ShiftedHom X Y a),
f = f_1 → ∀ (g g_1 : CategoryTheory.ShiftedHom Y Z b), g = g_1 → ∀ (h : b + a = c), f.comp g h = f_1.comp g_1 h- Defined in
- Mathlib.CategoryTheory.Shift.ShiftedHom
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- AddMonoidstatement and proof · cited by 2,864
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.ShiftedHomstatement and proof · cited by 88
- CategoryTheory.ShiftedHom.compstatement and proof · cited by 54
Cited by37
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.mk₀_comp_mk₀proof · cited by 10
- CategoryTheory.Abelian.Ext.zero_compproof · cited by 10
- CategoryTheory.Abelian.Ext.comp_zeroproof · cited by 7
- CategoryTheory.Abelian.Ext.mk₀_id_compproof · cited by 5
- CategoryTheory.Abelian.Ext.comp_mk₀_idproof · cited by 5
- CategoryTheory.Abelian.Ext.smul_homproof · cited by 4
- CategoryTheory.Abelian.Ext.add_homproof · cited by 4
- CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_homproof · cited by 3
- CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMapproof · cited by 3
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_homproof · cited by 3
- CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shiftproof · cited by 3
- CategoryTheory.Abelian.Ext.singleFunctor_map_comp_homproof · cited by 3