category of vector spaces

 algebra
Notation VectK\Vect_K Objects vector spaces over a field KK Morphisms linear maps Parent R−ModR{-}\Mod Related R−ModR{-}\Mod, FinVectK\FinVect_K, FiltVectK\FiltVect_K, FreeAb\FreeAb, VectKc\Vect^\c_K, VectKs\Vect^s_K, VectK(I)\Vect^{(I)}_K External nLab link
This is the special case of R−ModR{-}\Mod where RR is a field KK. It is the prototype of a split abelian category.

Satisfied properties

Assigned properties

Properties from parent

Deduced properties

Unsatisfied properties

Assigned properties

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Properties from parent

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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Special objects

  • terminal object: trivial vector space
  • initial object: trivial vector space
  • products: direct products with pointwise operations
  • coproducts: direct sums

Special morphisms

Indistinguishable categories

These categories in the database currently have exactly the same properties as the category of vector spaces. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.

Functors

The database stores 1 functor based on the category of vector spaces.

Symmetric monoidal categories

The database stores 1 symmetric monoidal category based on the category of vector spaces.