Categories for Family

[mkoeppe]

Currently a LazyFamily is automatically in EnumeratedSets, so at most countable.

We add keyword category to the constructor Family and all implementation classes, so that the user can choose the correct category.

Moreover, we define a (non-full) subcategory of Sets named Families, which captures the additional structure (= the map from the keys onto the parent).

Follow-ups / related:

• If the function from indices to objects is a morphism, then the category can be taken from the codomain.
• category of lazy family wrong if infinite combinatorial class used as index #18849 category of lazy family wrong if infinite combinatorial class used as index
• Bug in Family constructor #8822 Bug in Family constructor

Depends on #34375

CC: @tscrim

Component: combinatorics

Work Issues: Add method "as_map"

Author: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/34340

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,4 +1,6 @@
 Currently a `LazyFamily` is in `EnumeratedSets`, so at most countable.
 
+We add keyword `category` to `LazyFamily` (and the constructor `Family`) so that the user can choose the correct category.
 
+Also, if the `function` from indices to objects is a morphism, then the category can be taken from the codomain.
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -4,3 +4,4 @@
 
 Also, if the `function` from indices to objects is a morphism, then the category can be taken from the codomain.
 
+In fact, a `LazyFamily` is the same as an `ImageSubobject`. We unify these two concepts

[mkoeppe]

Branch: u/mkoeppe/lazyfamily__accept_category_keyword

[mkoeppe]

Commit: 6de0424

[mkoeppe]

New commits:

6de0424

Family: Pass keyword 'category' through to implementation classes

[mkoeppe]

Description changed:

--- 
+++ 
@@ -4,4 +4,4 @@
 
 Also, if the `function` from indices to objects is a morphism, then the category can be taken from the codomain.
 
-In fact, a `LazyFamily` is the same as an `ImageSubobject`. We unify these two concepts
+In fact, a `LazyFamily` is very similar to an `ImageSubobject`. We unify these two concepts

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5809547

src/sage/sets/family.py: Expand doc, clarify relationship to collections.abc and the Sets() category

[sagetrac-git]

Changed commit from 6de0424 to 5809547

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

18937bb

src/sage/sets/family.py: Accept init arg 'category' in Family implementation classes

[sagetrac-git]

Changed commit from 5809547 to 18937bb

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

96dd8ca

src/sage/sets/family.py: Update copyright according to git blame -w --date=format:%Y FILE | sort -k2

[sagetrac-git]

Changed commit from 18937bb to 96dd8ca

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9efef62

src/sage/sets/family.py: Improve some docstring markup

[sagetrac-git]

Changed commit from 96dd8ca to 9efef62

[mkoeppe]

Author: Matthias Koeppe