Wikidata:Property proposal/underlying structure

‎underlying structure edit

Originally proposed at Wikidata:Property proposal/Natural science

Done: underlying structure(s) (P12322) (Talk and documentation)

Description	an instance of the subject becomes an instance of the object if some of its data are lost
Represents	forgetful functor (Q2646117)
Data type	Item
Domain	mathematical structure (Q748349)
Allowed values	mathematical structure (Q748349)
Example 1	metric space (Q180953)underlying structureuniform space (Q652446)
Example 2	Lie group (Q622679)underlying structuresmooth manifold (Q78338964)
Example 3	Lie group (Q622679)underlying structuretopological group (Q1046291)
Example 4	graph (Q141488)underlying structureset (Q36161)
Example 5	ring (Q161172)underlying structureabelian group (Q181296)
Example 6	ring (Q161172)underlying structuremonoid (Q208237)

Motivation edit

The statement metric space (Q180953)subclass of (P279)topological space (Q179899) is strictly speaking not true, because a topological space, even if it "underlies" a metric space, does not have the metric data by which it becomes a metric space. What this statement really wants to say is that metric spaces are topological spaces if we decide to only consider the induced topology. This motivates me to propose a weaker property called "underlying structure". This property is not vague: if there is a faithful functor from the category of A to the category of B, we say Aunderlysing structureB; if further this functor is the inclusion from a subcategory (edit: or if the functor is fully faithful), we may use Asubclass of (P279)B (as in Hausdorff space (Q326908)subclass of (P279)topological space (Q179899)). To simplify the whole data graph of Wikidata we can make it a transitive Wikidata property, and make each statment in each entity in its strongest form (e.g. metric space (Q180953)underlying structuremetrizable space (Q1194053). 慈居 (talk) 07:42, 7 July 2023 (UTC)[reply]

Discussion edit

Question How much do we currently use subclass of (P279) for this? Is P279 an alternative? Answered in proposal. Jheald (talk) 18:52, 17 July 2023 (UTC)[reply]
The property subclass of (P279) will be fine if we are allowed to specify how many functors are there (as in bimodule (Q2903821)subclass of (P279)module (Q18848)quantity (P1114)2), or in which sense the statement holds (as in metric space (Q180953)subclass of (P279)metrizable space (Q1194053)criterion used (P1013)faithful functor (Q12175350) and in commutative ring (Q858656)subclass of (P279)ring (Q161172)criterion used (P1013)fully faithful functor (Q120721906)). Actually I will prefer this alternative if this is allowed, but I'm not sure. 慈居 (talk) 22:16, 17 July 2023 (UTC)[reply]

Currently subclass of (P279) seems used most commonly (Lie group (Q622679)); has part(s) of the class (P2670) is also used but less often (ring (Q161172)). The property has part(s) of the class (P2670) requires the subject to be an instance, not a class, so I think it does not fit this purpose. 慈居 (talk) 22:31, 17 July 2023 (UTC)[reply]

Another concern for subclass of (P279) is that statments like ring (Q161172)subclass of (P279)abelian group (Q181296) and ring (Q161172)subclass of (P279)monoid (Q208237) together may confuse people since all abelian groups are monoids; the latter statement might seem redundant and get deleted. 慈居 (talk) 22:56, 17 July 2023 (UTC)[reply]
Support, an important property for mathematics.--Arbnos (talk) 14:39, 11 January 2024 (UTC)[reply]
@慈居, Arbnos: Done --Tinker Bell ★ ♥ 00:33, 22 January 2024 (UTC)[reply]