Improve documentation of CategoryObject

[mkoeppe]

CategoryObject introduces itself as "an object in some category", but this is highly ambiguous.

In this ticket, we update the documentation along the following lines:

• keep a clear distinction between a Python object and a mathematical object
• acknowledge that "the same" mathematical object can be represented by several Python objects simultaneously
• acknowledge that "the" category of a mathematical object is not a meaningful mathematical concept; if one refers to it, it means that one is implicitly talking about a pair (object, category)
• reference the is-a/has-a distinction in object oriented programming
• finally explain that an instance of (a subclass of) CategoryObject
  • is a Python object
  • that has a distinguished/default category as its attribute _category (returned by the method category())
  • that mixes in attributes/methods from that category's ParentMethods.
• conclude that "the same" mathematical object can be represented by several instances of (subclasses of) CategoryObject for the purpose of "considering it as an object of" the category.

Related:

• 31247 Meta-ticket: ForgetfulFunctor not working properly

CC: @tscrim @xcaruso @DavidAyotte

Component: categories

Issue created by migration from https://trac.sagemath.org/ticket/34540

[mkoeppe]

Description changed:

--- 
+++ 
@@ -8,7 +8,7 @@
 - finally explain that an instance of (a subclass of) `CategoryObject` 
   - is a Python object 
   - that *has* a distinguished/default category as its attribute `_category` (returned by the method `category()`)
-  - that mixes in attributes/methods from that category.
+  - that mixes in attributes/methods from that category's `ParentMethods`.
 - conclude that "the same" mathematical object can be represented by several instances of (subclasses of) `CategoryObject` for the purpose of "considering it as an object of" the category. 

 Related: