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The category of fields of characteristic zero - #354

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ScriptRaccoon merged 2 commits into
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field-char-zero
Sep 5, 2026
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The category of fields of characteristic zero#354
ScriptRaccoon merged 2 commits into
mainfrom
field-char-zero

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@ScriptRaccoon ScriptRaccoon commented Sep 5, 2026

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This PR adds the category Fld0 of fields of characteristic zero. It provides an example of a balanced category that is not mono-regular; no category in the database has previously witnessed this combination (or its dual).

In fact, several additional new combinations are witnessed. The combination script (cf. #352) reveals the following:

Found 12 unique witnessed combinations by the supplied structures (Fld_0):

Directly witnessed:
- balanced ∧ ¬mono-regular
- epi-regular ∧ ¬mono-regular
- quotient-trivial ∧ ¬cogenerating set
- quotient-trivial ∧ ¬essentially small
- quotient-trivial ∧ ¬extremal cogenerating set
- quotient-trivial ∧ ¬mono-regular

Dually witnessed:
- balanced ∧ ¬epi-regular
- mono-regular ∧ ¬epi-regular
- subobject-trivial ∧ ¬generating set
- subobject-trivial ∧ ¬essentially small
- subobject-trivial ∧ ¬extremal generating set
- subobject-trivial ∧ ¬epi-regular

Moreover, the obvious implication subobject-trivial => well-powered has been added (and hence also its dual).

The number of unwitnessed consistent combinations has decreased from 701 to 687.

This PR contributes to this milestone.

@ScriptRaccoon
ScriptRaccoon merged commit 1484202 into main Sep 5, 2026
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ScriptRaccoon deleted the field-char-zero branch September 5, 2026 09:42
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