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Add two categories of finitely generated projective modules - #350

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ScriptRaccoon merged 6 commits into
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finite-projective-modules
Sep 3, 2026
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Add two categories of finitely generated projective modules#350
ScriptRaccoon merged 6 commits into
mainfrom
finite-projective-modules

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@ScriptRaccoon ScriptRaccoon commented Sep 3, 2026

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This PR adds two instances of the category of finitely generated projective modules over a ring: one over the ring of integers and one over the ring of dual numbers. All properties have been decided.

We now have exactly 100 categories in the database. 🎉

One could try to add the category Projfg(R) of finitely generated projective modules over a ring more generally, but many properties cannot be decided in this generality. The two examples already indicate a significant difference. For example, Projfg(R[ε]) is balanced, but Projfg(Z) is not.

New property combinations

  • The category Projfg(Z) = FreeAbfg provides an example of an additive category that is not balanced and does not have coproducts.
  • The category Projfg(R[ε]) provides an example of an additive, normal, and conormal category that is not abelian.

For combinations of the form "p and not q", the number of consistent yet unwitnessed combinations went down from 733 to 725. The combinations script shows:

Found 4 unique witnessed combinations for category with ID "FreeAb_fg":
- essentially countable ∧ ¬effective cocongruences
- essentially countable ∧ ¬effective congruences
- self-dual ∧ ¬effective cocongruences
- self-dual ∧ ¬effective congruences
Found 4 unique witnessed combinations for category with ID "Proj_fg(Re)":
- normal ∧ ¬coreflexive equalizers
- normal ∧ ¬reflexive coequalizers
- conormal ∧ ¬coreflexive equalizers
- conormal ∧ ¬reflexive coequalizers

@ScriptRaccoon
ScriptRaccoon force-pushed the finite-projective-modules branch from 32831c0 to b8f6e38 Compare September 3, 2026 15:21
@ScriptRaccoon ScriptRaccoon changed the title Add the categories of finitely generated projective modules over the integers and the ring of dual numbers Add two categories of finitely generated projective modules Sep 3, 2026
@ScriptRaccoon
ScriptRaccoon merged commit f5fc4c0 into main Sep 3, 2026
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ScriptRaccoon deleted the finite-projective-modules branch September 3, 2026 15:24
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