Theorems · Inductive type · group theory
ZeroHom
(M : Type u_10) → (N : Type u_11) → [Zero M] → [Zero N] → Type (max u_10 u_11)
ZeroHom M N is the type of functions M → N that preserve zero.
When possible, instead of parametrizing results over (f : ZeroHom M N),
you should parametrize over (F : Type*) [ZeroHomClass F M N] (f : F).
When you extend this structure, make sure to also extend ZeroHomClass.
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 161 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
Around this declaration
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by231
Results whose statement or proof uses this declaration.
- ArithmeticFunctionproof · cited by 290
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- MonoidWithZeroHom.ofClassproof · cited by 204
- ZeroHom.toFunstatement and proof · cited by 101
- HahnSeries.singlestatement · cited by 82
- AddMonoidHom.toZeroHomstatement · cited by 61
- DFinsupp.sumAddHomproof · cited by 38
- MonoidWithZeroHom.toZeroHomstatement · cited by 35
- ZeroHom.mk.congr_simpstatement · cited by 20
- DistribSMul.toAddMonoidHomproof · cited by 20
- AddMonoidHom.singleproof · cited by 19
- ZeroHom.compstatement and proof · cited by 16
Showing the 200 most cited of 231.