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3. Functors 

This section provides information about functors.

3.1 Summary

3.2 Example. (Calculation of Hom(Z/12Z + Z, -) Functor

3.3 Other functors

 

3.1 Summary

This software supports covariant functors of tensor product, Tor(A, -), Hom(A, -), Ext(A,-) and contavariant Hom(-,A), Ext(-,A). If you wish to calculate a functor then you should select a group of objects and then calucate the fucntor.

3.2 Example. (Calculation of Hom(Z/12Z + Z, -) Functor)

Step 1.

Select a diagram of abelian gruops. For example:

 

Step 2.

Create a group Z/12Z + Z.

 

Step 3.

 

Put the functor square (left) to desktop and link it with the group square(right).

 

Step 4.

Open the functor properties editor. Check the "Covariant" checkbox and press the "Perform functor from selected" button. It results to

 

Right down shifted, unselected squares represent result of functor calculation

 

3.3 Other Functors

Other functors may be calculated by choosing suboptions of menu option "Functors". The algoritm is simple. Select objects and morphisms and then choose menu option.



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