Discrete Lawvere theories and computational effects (Q860883)

Lawvere theories are a category-theoretic formulation of universal algebra for which the notion of operation is primitive. Countable Lawvere theories allow for the modelling of several computational effects in terms of sums, tensors and distributive tensors. The enrichment of a category allows to extend the type of computational effects that can be modelled. For countable Lawvere theories, sums and tensors extend to the enriched version, but distributive tensors do not. In this paper, the authors modify the notion of enriched Lawvere theory, introducing the discrete Lawvere theory, so that it is possible to incorporate an enriched account of the distributive tensor.