# Category: Ab

Ab is the category whose objects are Abelian groups and arrows are group maps.

## Facts Derived from Enrichment

Ab has a zero morphism between any two objects (enriched in Set*).

Ab is a closed category (enriched in itself).

Every object in Ab is a ring (enriched in Ab).

## Notable Subcategories

- Ab (groups)
- AbTor (plain)
- AbTorF (reflection)
- CMon (plain)
- CRing (commutative monoids)
- LieRing (Lie algebras)
- Ring (monoids)

## Limits

Has all finite limits and a zero object

## Colimits

Has all finite colimits and a zero object

# categories: Ab

This data as json

name | objects_hr | arrows_hr |
---|---|---|

Ab | Abelian groups | group maps |

## Links from other tables

- 0 rows from internal_commutative_monoids in categories_of_commutative_monoids
- 1 row from parent in categories_of_commutative_monoids
- 0 rows from completion in karoubi_envelopes
- 0 rows from category in karoubi_envelopes
- 0 rows from internal_semigroups in categories_of_semigroups
- 0 rows from parent in categories_of_semigroups
- 2 rows from category in enrichments
- 4 rows from homs in enrichments
- 0 rows from internal_relations in bicategories_of_relations
- 0 rows from parent in bicategories_of_relations
- 8 rows from category in categorical_structure
- 0 rows from subcategory in subcategories
- 2 rows from parent in subcategories
- 0 rows from groupoid in cores
- 0 rows from category in cores
- 0 rows from internal_monoids in categories_of_monoids
- 1 row from parent in categories_of_monoids
- 0 rows from internal_rings in categories_of_rings
- 0 rows from parent in categories_of_rings
- 0 rows from skeleton in skeletons
- 0 rows from category in skeletons
- 0 rows from partial_category in restriction_categories
- 0 rows from total_subcategory in restriction_categories
- 0 rows from category in topoi
- 0 rows from category in monoidal_categories
- 0 rows from supercategory in full_subcategories
- 0 rows from subcategory in full_subcategories
- 0 rows from supercategory in essentially_wide_subcategories
- 0 rows from subcategory in essentially_wide_subcategories
- 0 rows from category in disconnected_categories
- 0 rows from pointed in maybe_monads
- 0 rows from base in maybe_monads
- 0 rows from monoids in list_monads
- 0 rows from base in list_monads
- 0 rows from multisets in multiset_monads
- 0 rows from base in multiset_monads
- 1 row from parent in categories_of_lie_algebras
- 0 rows from internal_lie_algebras in categories_of_lie_algebras
- 0 rows from parent in categories_of_abelian_groups
- 1 row from internal_abelian_groups in categories_of_abelian_groups
- 1 row from parent in categories_of_simplicial_objects
- 0 rows from internal_simplicial_sets in categories_of_simplicial_objects
- 0 rows from category in categories_with_animal_names
- 3 rows from internal_groups in categories_of_groups
- 1 row from parent in categories_of_groups
- 1 row from supercategory in reflective_subcategories
- 1 row from subcategory in reflective_subcategories
- 0 rows from horizontal_2cat in double_categories
- 0 rows from vertical_2cat in double_categories
- 0 rows from example_categeory in logical_completeness
- 0 rows from complete_2category in logical_completeness
- 0 rows from category in arrow_categories
- 0 rows from arrows in arrow_categories
- 0 rows from op in opposite_categories
- 0 rows from category in opposite_categories
- 0 rows from category in dagger_categories
- 0 rows from name in 2-categories