COLIMITS IN THE CATEGORY OF QUADRATIC MODULES

Abstract

To use of colimits to put structures together is not uncommon in mathematics; coproducts particularly of structures such as groups and vector spaces have been known for a long time. Colimits have also been used in computer science for example to put together labeled graphs, in system theory etc. The importance of category for theoretical computer scientists is everyday increasing. In order to contribute usage of colimits, we show existence of finite (co)limits in the category of quadratic modules of groups by careful construction of (co)product object and (co)equilaser of morphisms of quadratic modules. Moreover, we give some examples of coproduct.