Contribution
Equational properties of iteration in algebraically complete categories

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Abstract

We prove the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.

Keywords

Fixed points
Iteration theories
Algebraically complete categories

Cited by (0)

1

Partially supported by grant no. T22423 of the National Foundation of Hungary for Scientific Research, and by the US-Hungarian Joint Fund under grant no. 351.

2

Partially supported by the EEC IICM project EXPRESS.