Structures · Category theory
CategoryTheory.AddModObj
Given an action of a monoidal category C on a category D,
an action of an additive monoid object M in C on an object X in D is the data of a
map vadd : M ⊙ₗ X ⟶ X that satisfies zero-additivity and associativity with addition.
See AddAction for the non-categorical version.
- Defined in
- Mathlib.CategoryTheory.Monoidal.Mod
- Shape
- 2 explicit arguments · adds vadd, zero_vadd, add_vadd
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Extended by0
Nothing extends this class yet.
Concrete types that are instances0
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Assumed by29
- CategoryTheory.AddModObj.vadd
- CategoryTheory.AddMod.scalarRestriction
- CategoryTheory.AddModObj.add_vadd
- CategoryTheory.AddModObj.zero_vadd
- CategoryTheory.AddModObj.add_vadd_self
- CategoryTheory.AddModObj.zero_vadd_self
- CategoryTheory.AddMod.scalarRestriction_vadd
- CategoryTheory.IsAddModHom.map_vadd
- CategoryTheory.AddModObj.ofIso
- CategoryTheory.AddModObj.add_vadd_self_flip
- CategoryTheory.IsAddModHom.addActionHom
- CategoryTheory.AddMod.Hom.mk''
- CategoryTheory.instIsAddModHomNegOfHom
- CategoryTheory.AddMod.scalarRestriction_hom
- CategoryTheory.instIsAddModHomComp
- CategoryTheory.AddMod.Hom.mk''_hom
- CategoryTheory.Hom.vadd_def
- CategoryTheory.AddModObj.ofIso_vadd
- CategoryTheory.AddModObj.add_vadd_assoc
- CategoryTheory.AddModObj.zero_vadd_assoc
- CategoryTheory.Hom.addAction
- CategoryTheory.AddModObj.add_vadd_self_assoc
- CategoryTheory.IsAddModHom.map_vadd_assoc
- CategoryTheory.AddModObj.add_vadd_self_flip_assoc
- CategoryTheory.AddModObj.zero_vadd_self_assoc
- CategoryTheory.AddModObj.assoc_flip
- CategoryTheory.instIsAddModHomId
- CategoryTheory.Hom.instVAddHom
- CategoryTheory.IsAddModHom.addActionHom_apply
Ancestors0
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