Opened 7 years ago

Last modified 3 years ago

## #20515 new enhancement

# Proper idiom for defining an axiom as the intersection of two axioms defined in the same category.

Reported by: | nthiery | Owned by: | |
---|---|---|---|

Priority: | minor | Milestone: | sage-wishlist |

Component: | categories | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

Let `Cs`

be a category, where three axioms are defined, `A`

, `A1`

,
`A2`

, with `A`

being the intersection of `A1`

and `A2`

. The natural
implementation would look like:

from sage.categories.category_with_axiom import CategoryWithAxiom, all_axioms all_axioms += ("A", "A1", "A2") class Cs(Category): def super_categories(self): return [Objects()] class SubcategoryMethods: def A1(self): return self._with_axiom("A1") def A2(self): return self._with_axiom("A2") def A(self): return self._with_axiom("A") class A1(CategoryWithAxiom): pass class A2(CategoryWithAxiom): def A1_extra_super_categories(self): return [Cs().A()] class A(CategoryWithAxiom): def extra_super_categories(self): return [Cs().A1(), Cs().A2()]

However this triggers an infinite recursion loop:

sage: Cs().A() RuntimeError: maximum recursion depth exceeded while calling a Python object

This is because `Cs().A2().A1_extra_super_categories()`

does not
return a strict super category of the to-be-constructed category,
which is forbidden by the current specifications:

http://doc.sagemath.org/html/en/reference/categories/sage/categories/category_with_axiom.html#id2

A workaround is to define `A`

(or `A1`

, or `A2`

) in some super category:

class C0(Category): def super_categories(self): return [Objects()] class SubcategoryMethods: def A(self): return self._with_axiom("A") class A(CategoryWithAxiom): pass class C1(Category): def super_categories(self): return [C0()] class SubcategoryMethods: def A1(self): return self._with_axiom("A1") def A2(self): return self._with_axiom("A2") class A1(CategoryWithAxiom): pass class A2(CategoryWithAxiom): def A1_extra_super_categories(self): return [C0.A()] class A(CategoryWithAxiom): def extra_super_categories(self): return [C1.A1(), C1.A2()]

Then,

sage: C1().A1().A2() is C1().A() True sage: C1().A() Category of a1 a2 c1 sage: C1().A().super_categories() [Category of a c0, Category of a2 c1, Category of a1 c1] sage: C1().A1().A2() is C1().A() True

See #18265 for a concrete instance where this workaround is currently
used when none of `A`

, `A1`

, `A2`

make sense in a strict super category.
A better idiom would be desirable if more use cases appear.

### Change History (2)

### comment:1 Changed 7 years ago by

Description: | modified (diff) |
---|

### comment:2 Changed 3 years ago by

Milestone: | sage-7.2 → sage-wishlist |
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