Category: Vect_k

Vect_k is the category whose objects are vector spaces over fields k and arrows are linear maps.

Facts Derived from Enrichment

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

Vect_k is a closed category (enriched in itself).

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

Every object in Vect_k is a k-algebra (enriched in Vect_k).

Notable Subcategories

• CartSp (plain)
• FinVect_k (full)
• LieAlg_k (Lie algebras)

Limits

Has all finite products

Colimits

Has all finite sums

categories: Vect_k

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