A DIAMOND LEMMA FOR HECKE-TYPE ALGEBRAS

In this paper we give a version of Bergman's diamond lemma which applies to certain monoidal categories presented by generators and re-lations. In particular, it applies to: the Coxeter presentation of the symmetric groups, the quiver Hecke algebras of Khovanov-Lauda-Rouquier, the Webster tensor product algebras, and various generalizations of these. We also give an extension of Manin-Schechtmann theory to non-reduced expressions.