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Theorems · Theorem · category theory

AddCommGrpCat.subsingleton_of_isZero

∀ {G : AddCommGrpCat}, CategoryTheory.Limits.IsZero G → Subsingleton ↑G
Defined in
Mathlib.Algebra.Category.Grp.Zero
Cited by
4 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddCommGrpCat.isZero_iff_subsingleton · cited by 1AddCommGrpCat.isZero_iff_…ModuleCat.subsingleton_ext_of_exists_isRegular · cited by 1ModuleCat.subsingleton_ex…ModuleCat.exists_isRegular_of_exists_subsingleton_ext · cited by 1ModuleCat.exists_isRegula…CategoryTheory.Sheaf.subsingleton_H_of_isZero · cited by 0Sheaf.subsingleton_H_of_i…AddCommGrpCat · cited by 462AddCommGrpCatAddCommGrpCat.carrier · cited by 407AddCommGrpCat.carrierCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroAddEquiv.toEquiv · cited by 174AddEquiv.toEquivAddCommGrpCat.of · cited by 97AddCommGrpCat.ofEquiv.subsingleton · cited by 24Equiv.subsingletonCategoryTheory.Limits.IsZero.iso · cited by 11IsZero.isoCategoryTheory.Iso.addCommGroupIsoToAddEquiv · cited by 7Iso.addCommGroupIsoToAddE…AddCommGrpCat.isZero_of_subsingleton · cited by 4AddCommGrpCat.isZero_of_s…AddCommGrpCat.subsingleton_of…CITED BYCITES

Cites9

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Cited by4

Results whose statement or proof uses this declaration.