Matches in DBpedia 2015-04 for { <http://dbpedia.org/resource/Category_of_vector_spaces> ?p ?o }
Showing triples 1 to 21 of
21
with 100 triples per page.
- Category_of_vector_spaces abstract "In mathematics, especially category theory, the category K-Vect (some authors use VectK) has all vector spaces over a fixed field K as objects and K-linear transformations as morphisms. If K is the field of real numbers, then the category is also known as Vec.Since vector spaces over K (as a field) are the same thing as modules over the ring K, K-Vect is a special case of R-Mod, the category of left R-modules. K-Vect is an important example of an abelian category.Much of linear algebra concerns the description of K-Vect. For example, the dimension theorem for vector spaces says that the isomorphism classes in K-Vect correspond exactly to the cardinal numbers, and that K-Vect is equivalent to the subcategory of K-Vect which has as its objects the free vector spaces Kn, where n is any cardinal number.There is a forgetful functor from K-Vect to Ab, the category of abelian groups, which takes each vector space to its additive group. This can be composed with forgetful functors from Ab to yield other forgetful functors, most importantly one to Set.K-Vect is a monoidal category with K (as a one-dimensional vector space over K) as the identity and the tensor product as the monoidal product.".
- Category_of_vector_spaces wikiPageID "337590".
- Category_of_vector_spaces wikiPageRevisionID "626047617".
- Category_of_vector_spaces hasPhotoCollection Category_of_vector_spaces.
- Category_of_vector_spaces subject Category:Category-theoretic_categories.
- Category_of_vector_spaces subject Category:Linear_algebra.
- Category_of_vector_spaces type Abstraction100002137.
- Category_of_vector_spaces type Category-theoreticCategories.
- Category_of_vector_spaces type Class107997703.
- Category_of_vector_spaces type Collection107951464.
- Category_of_vector_spaces type Group100031264.
- Category_of_vector_spaces comment "In mathematics, especially category theory, the category K-Vect (some authors use VectK) has all vector spaces over a fixed field K as objects and K-linear transformations as morphisms. If K is the field of real numbers, then the category is also known as Vec.Since vector spaces over K (as a field) are the same thing as modules over the ring K, K-Vect is a special case of R-Mod, the category of left R-modules.".
- Category_of_vector_spaces label "Categorie van vectorruimten".
- Category_of_vector_spaces label "Category of vector spaces".
- Category_of_vector_spaces sameAs Categorie_van_vectorruimten.
- Category_of_vector_spaces sameAs m.01xpsh.
- Category_of_vector_spaces sameAs Q5051857.
- Category_of_vector_spaces sameAs Q5051857.
- Category_of_vector_spaces sameAs Category_of_vector_spaces.
- Category_of_vector_spaces wasDerivedFrom Category_of_vector_spaces?oldid=626047617.
- Category_of_vector_spaces isPrimaryTopicOf Category_of_vector_spaces.