# Category: FinVect_k

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

## Facts Derived from Enrichment

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

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

## Notable Subcategories

- FinVect_q (full)
- Mat_k (equivalence)
- Mat_k (skeleton)

## Limits

Has a terminal object which is a zero object

## Colimits

Has an initial object which is a zero object

# categories: FinVect_k

This data as json

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

FinVect_k | finite vector spaces over fields k | linear maps |

## Links from other tables

- 0 rows from internal_commutative_monoids in categories_of_commutative_monoids
- 0 rows 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
- 0 rows from homs in enrichments
- 0 rows from internal_relations in bicategories_of_relations
- 0 rows from parent in bicategories_of_relations
- 2 rows from category in categorical_structure
- 0 rows from subcategory in subcategories
- 0 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
- 0 rows 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
- 1 row 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
- 1 row from supercategory in full_subcategories
- 1 row 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
- 0 rows 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
- 0 rows from internal_abelian_groups in categories_of_abelian_groups
- 0 rows 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
- 0 rows from internal_groups in categories_of_groups
- 0 rows from parent in categories_of_groups
- 0 rows from supercategory in reflective_subcategories
- 0 rows from subcategory in reflective_subcategories
- 0 rows from horizontal_2cat in double_categories
- 0 rows from vertical_2cat in double_categories
- 2 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