2. Objects and Morphisms. 

This section provides information about objects and morphisms.

2.1 Abelian groups

2.2 Vector spaces

2.3 Finitely generated algebras

2.3 Finite sets

 

2.1 Abelian groups

The framework operates, in particular, with category of finitely generated Abelian groups. The icon corresponds to Abelian group. The properties editor of this object is shown on the following picture.

This editor enables to enter number of generators and relations between them. It shows the group rank and primary components. The corresponds to homomorphism of this category. Followng picture shows the properties editor of the homomorphism.

User can set a homorphism both by generators or primary components. The editror also provides Ker, Coker and Image of  homorrphism creation. 

2.2 Vector spaces

The buttons   c   corresponds to vector space over rational and Galois fields respectively. Properties editors of these spaces enables editing of their dimension and field characteristic. The   button corresponds to homomorphism of this category. It's property editor provides homomorphism properties editing by the following way. 

 

2.3 Finitely generated algebras

 The button corresponds to commutative finitely generated Q algebra. Its properies etitor is shown on the following picture. 

This editor provides editing the number of generators and relations between them. The corresponds to commutative algebra homomorphism. It's properties editor is shown on the following picture.

This editor provides the definition of homomorpism by it's generators.

2.4 Finite sets