# 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

This data as json

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

Vect_k | vector spaces over fields k | linear maps |

## Links from other tables

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