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

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Links from other tables

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