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Add the category of large families of vector spaces with ess. small support - #365

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large-families-vector-spaces
Sep 11, 2026
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Add the category of large families of vector spaces with ess. small support#365
ScriptRaccoon merged 1 commit into
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large-families-vector-spaces

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@ScriptRaccoon ScriptRaccoon commented Sep 9, 2026

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This PR adds an example of a split abelian, complete and cocomplete category that does not have a generator (and no cogenerator). The category is Vect(I) for a collection I that is not essentially small. Objects are I-indexed families of vector spaces whose support is essentially small (i.e. isomorphic to a set).

The number of missing combinations went down from 495 to 481.

Found 14 unique witnessed combinations by the supplied structures (Vect_family):

Directly witnessed:
- CIP ∧ ¬generating set
- CIP ∧ ¬generator
- exact filtered colimits ∧ ¬generating set
- split abelian ∧ ¬cogenerating set
- split abelian ∧ ¬cogenerator
- split abelian ∧ ¬extremal cogenerating set
- split abelian ∧ ¬extremal cogenerator
- split abelian ∧ ¬extremal generating set
- split abelian ∧ ¬extremal generator
- split abelian ∧ ¬generating set
- split abelian ∧ ¬generator

Dually witnessed:
- CSP ∧ ¬cogenerating set
- CSP ∧ ¬cogenerator
- exact cofiltered limits ∧ ¬cogenerating set

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ScriptRaccoon force-pushed the large-families-vector-spaces branch 2 times, most recently from 9aeeaf5 to 0410820 Compare September 10, 2026 17:58
@ScriptRaccoon ScriptRaccoon changed the title Add the category of large families of vector spaces with small support Add the category of large families of vector spaces with ess. small support Sep 11, 2026
@ScriptRaccoon
ScriptRaccoon force-pushed the large-families-vector-spaces branch from 0410820 to 3ff1e15 Compare September 11, 2026 16:35
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ScriptRaccoon marked this pull request as ready for review September 11, 2026 17:36
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ScriptRaccoon force-pushed the large-families-vector-spaces branch from 3ff1e15 to 733e6b5 Compare September 11, 2026 17:37
@ScriptRaccoon
ScriptRaccoon force-pushed the large-families-vector-spaces branch from 733e6b5 to 34435cb Compare September 11, 2026 17:39
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ScriptRaccoon merged commit eea0ffc into main Sep 11, 2026
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ScriptRaccoon deleted the large-families-vector-spaces branch September 11, 2026 17:43
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