This page gives a description of the category tree structure on the Group Properties Wiki.
Some things to know right away
What the software provides
A category is, roughly, a list of articles. In addition to this, a category can have subcategories, and each of these subcategories itself stores a list of articles.
Every category has a category page; for instance, Category:Variations of normality. The category page usually has the following:
- Some explanatory text on what the category is about
- A list of subcategories of the category. By clicking on the "+" next to any subcategory, one can see the subcategories within that subcategory
- A list of all articles directly in the category
- At the bottom, a list of categories in which the category lies
At the bottom of every article, is a list of all the categories in which it lies. Clicking on any of these categories takes one to the category page.
The choices made here
Here, we have adopted two kinds of categories:
- The first are the genuine categories, i.e. categories which contain articles. The convention adopted for these categories is that, unless there are other reasons, any article included in a subcategory should also be in the category. Thus, if Category:Transitive subgroup properties is a subcategory of Category:Subgroup properties, you'll find all the transitive subgroup properties also listed as subgroup properties.
- The second are supercategories. Their purpose is only to list categories and aid in categorytree navigation. They do not list any articles. Examples are Category:Properties.
This dichotomy we have chosen here is by no means standard. It is possible that we'll change our approach once there is a better development and implementation of categories in the software.
The big supercategories
Remember that categorytree navigation is not meant to be the primary way to find information. The main exploratory tool is search, go to related pages, observe similarities and go on. Categorytree navigation is intended to complement this.
Articles on the Group Properties Wiki are classified with the following big labels:
- Terms/definitions: Groupprops:Definition article describes what such articles contain, and how they are organized. The supercategory for all terms/definitions is Category:Terminology
- Facts/theorems: Groupprops:Fact article describes what such articles contain, and how they are organized. The supercategory for all facts/theorems is Category:Facts
- Survey articles: Groupprops:Survey article describes what such articles contain, and how they are organized. The category for these is Category:Survey articles. This should soon become a supercategory; as of now, all articles in the category are listed because it is extremely small.
- Real-world entity articles: The category structure for these is still to be implemented
These supercategories are provided in the lookup menu on the left sidebar, so you can click on any of them any time.
Locating what you're looking for
Suppose you're looking for something like proofs of the kind which show that one group property implies the other. First, you'd click facts/theorems on the left sidebar, to reach Category:Facts. Now, go through the list of all the fact categories. A quick scan shows that what you're most likely to be looking for is in the category named Property implications. Clicking the "+" to expand it, you see exactly what you're looking for: Category:Group property implications.
The idea is to at each stage, scan and figure out what's closest, expand to see further subcategories, and then explore more.
Using the category tree for navigation is not the only way to find the relevant category or list you're looking for. There are other ways:
- By example: Suppose you have one example of the kind of thing you're looking for. Just go to that. Chances are that you'll see a box right on top, giving a link to the category of examples of the same sort. If not, go straight down to the list of categories of the article (given at the bottom of the page). And try to locate the category there.
- By contrast: Suppose what you're looking for is one property not implying the other, but you have in mind an example of one property impliying the other. Go to the page you know! You'd likely see a prominent link to the category you're looking for. For instance, characteristic implies normal has a box on top that links not only to the subgroup property implications, but also to the subgroup property non-implications.
- By analogy and relation: Look for things that use any similar idea, similar principle. For a specific term, look for the corresponding general term. For a general term, look for a corresponding specific term.
Other locator techniques
We also have a category specifically devoted to those categories that are organized around the property-theoretic paradigm. You can see this in the lookup in the left sidebar, as property-theoretic locator. This category lists both definition categories and fact categories that are organized based on the property-theoretic paradigm.
Categorytree navigation is still in its very initial stages, so expect significant improvements as time passes!