# SetsWithPartialMaps¶

class sage.categories.sets_with_partial_maps.SetsWithPartialMaps(s=None)

The category whose objects are sets and whose morphisms are maps that are allowed to raise a ValueError on some inputs.

This category is equivalent to the category of pointed sets, via the equivalence sending an object X to X union {error}, a morphism f to the morphism of pointed sets that sends x to f(x) if f does not raise an error on x, or to error if it does.

EXAMPLES:

sage: SetsWithPartialMaps()
Category of sets with partial maps

sage: SetsWithPartialMaps().super_categories()
[Category of objects]


TESTS:

sage: TestSuite(SetsWithPartialMaps()).run()

class HomCategory(category, name=None)

Initializes this HomCategory

INPUT:
• category – the category whose Homsets are the objects of this category.
• name – An optional name for this category.

EXAMPLES:

We need to skip one test, since the hierarchy of hom categories isn’t consistent yet:

sage: C = sage.categories.category.HomCategory(Rings()); C
Category of hom sets in Category of rings
sage: TestSuite(C).run(skip=['_test_category_graph'])

SetsWithPartialMaps.super_categories()

EXAMPLES:

sage: SetsWithPartialMaps().super_categories()
[Category of objects]