Abstract rewriting internalized [article]

Maxime Lucas
2020 arXiv   pre-print
In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector space of relations. Strikingly, although both theories are very similar, most results (such as Newman's Lemma) require different proofs in these two settings. In this paper, we develop rewriting theory internally to a category C satisfying some mild properties. In this general setting, we define the notions of
more » ... ion, local confluence and confluence using the notion of reduction strategy, and prove an analogue of Newman's Lemma. In the case of C= Set or C = Vect we recover classical results of abstract and algebraic rewriting in a slightly more general form, closer to von Oostrom's notion of decreasing diagrams.
arXiv:2002.06004v1 fatcat:wlfy7zyftnhx7jt4tzfsd7dhba