Homotopy reduction systems for monoid presentations Asphericity and low-dimensional homology Original Research Article

Homotopy theory for monoid presentations originated by Squier is developed by means of homotopy reduction systems. Two types of asphericity are considered and a relation to the low-dimensional homology is established. If a monoid presentation has a complete homotopy reduction system that is essentially finite, then the monoid has the homology finiteness property FP4.