Theorems · Definition · category theory
ModuleCat.of
(R : Type u) → [inst : Ring R] → (X : Type v) → [inst_1 : AddCommGroup X] → [Module R X] → ModuleCat R
The object in the category of R-algebras associated to a type equipped with the appropriate
typeclasses. This is the preferred way to construct a term of ModuleCat R.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Basic
- Cited by
- 594 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 25 definitions · uses no axioms
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- ModuleCatstatement · cited by 1,429
Cited by745
Results whose statement or proof uses this declaration.
- ModuleCat.ofHomstatement · cited by 200
- CategoryTheory.ShortComplex.moduleCatLeftHomologyDataproof · cited by 106
- groupHomology.inhomogeneousChainsproof · cited by 90
- groupCohomology.inhomogeneousCochainsproof · cited by 83
- groupCohomology.cochainsIso₁statement · cited by 35
- Rep.Hom.toModuleCatHomstatement · cited by 34
- Rep.coinvariantsFunctorproof · cited by 34
- groupHomology.chainsIso₁statement · cited by 33
- groupCohomology.cochainsIso₀statement · cited by 32
- groupCohomology.d₀₁statement · cited by 32
- groupHomology.chainsIso₂statement · cited by 32
- groupHomology.d₁₀statement · cited by 29
Showing the 200 most cited of 745.