Groupprops:Metaproperty definition article

A metaproperty definition article is a definition article for a metaproperty. Since a metaproperty is after all a property (over a space which itself comprises properties) a metaproperty definition article can be viewed as a special instance of a property definition article.

All articles may not match the standards given here because these standards have themselves evolved along with groupprops. The article on transitive subgroup property shall be a prototype that shall always conform to the latest format, layout and standards.

Adjectival naming
Typically, a metaproperty is given by an adjective, followed by the term for a generic property. For instance, the subgroup metaproperty of being transitive is termed transitive subgroup property, here transitive is the adjective and subgroup property is the generic element of the space over which the property is defined.

Thus, if we are looking at properties over objects O, then the general name for a metaproperty would be (adjective for metaproperty) O property.

Member-noun naming
Here, the property is given by a noun, where the noun would be used for a typical element having the property.

We simply use the member noun as the article name.

Metaproperty-noun naming
Here, the metaproperty is given by a noun, where any element satisfying the property is said to satisfy the property noun. For instance, the term transitivity is a property noun for the property of being normal, and any subgroup which is normal is said to satisfy the property of normality.

We simply use the metaproperty noun as the article name.

By and large, adjectival naming is preferred, so if both adjectival naming and member/property noun naming is used, redirect from the member/property noun article to the adjectival naming article.

Templates

 * Use the appropriate metaproperty space specification template. A listing of property space specification templates is provided at:

Category: Metaproperty space specification templates


 * Apply general rules for deciding whether to use Template: Wikilocal, Template:Basicdef, Template:Semibasicdef and so on.


 * Check whether the term being defined is a variation of (in which case the template Template:Variationof is to be used) or an opposite of (in which case the template Template:Oppositeof is to be used) some more pivotal metaproperty.

History
Follow the same guidelines as for a general history section.

Definition
Follow the same guidelines as for a general definition, which are specified in the Groupprops:Definition article.

Relation with other properties
The section relation with other properties is intended to give some idea of where the given property lies, both in relation with other properties in the same property space, and in relation with properties/operators/elements outside.

If the metaproperty is pivotal, the section begins with the use of Template:Pivotalmetaproperty followed by a listing of the variation, opposites and other related categories. Subsections include:


 * Stronger metaproperties: Here, the stronger properties are stated in a list and for each one, a link to the proof may be provided if it exists
 * Conjunction with other metaproperties: Here, both the property with which conjunction is taken and the result of applying conjunction are specified
 * Weaker metaproperties: Here, the weaker properties are stated in a list and for each one, a link to the proof may be provided if it exists
 * Related metaproperties: This may describe other metaproperties that closely resemble the given one

Metametaproperties
Just like we can evaluate any given property with respect to a metaproperty, we can evaluate any given metaproperty with respect to a metametaproperty. The metametaproperties section contains a list of all the important metametaproperties, and discusses, in each subsection, whether the metaproperty satisfies the metametaproperty. The subsection should try to give a brief reason why the metaproperty is satisfied or not satisfied and a link to the article giving a proof/counterexample.

Note that the template for yes will also include the given property in the category of properties satisfying the given subgroup metaproperty.

The list of templates is available separately for each property space, and the list of these lists is at:

Category: Memetataproperty satisfaction template types

Metaproperty operators
This section describes the effect of various metaproperty operators and metaproperty modifiers on the given property. For each property operator, there is a corresponding template which writes an emphasized sentence on top saying that the effect of applying this modifier or operator is so-and-so.

The further content of the subsection provides a closer explanation of what is meant, and a link to the proof.

Property operators
This section discusses important property operators closely related to the given property. For instance, we are interested in:


 * property modifiers such that the image space for this is precisely the collection of properties satisfying the metaproperty
 * property modifiers such that the fixed point space for this is precisely the collection of properties satisfying the metaproperty
 * binary property operators that in some way yield the given metaproperty

Testing
The testing section describes any related computational problem and provides a Template:Further link for more information on the computational problem.