Varieties defined by natural transformations

Details Varieties defined by natural transformations Varieties defined by natural transformations

2009-04-10

arxiv.org/abs/0904.1678v1

Mathematics

Category Theory

16 pages, submitted to Archivum Mathematicum, Masaryk University, Brno, Czech Republic

Scientific paper

We define varieties of algebras for an arbitrary endofunctor on a cocomplete
category using pairs of natural transformations. This approach is proved to be
equivalent to the one of equational classes defined by equation arrows. Free
algebras in the varieties are investigated and their existence is proved under
the assumptions of accessibility.

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