On descent theory for monoid actions (Q1771119)

The paper contains some sufficient conditions for a monoid homomorphism to be an effective descent morphism. If \(f:R\to S\) is a monoid homomorphism such that \(S_R\) is equalizer flat and \(r\) is left invertible whenever \(f(r)\) is left invertible for every \(r\in R\), then \(f\) is an effective descent morphism (Proposition 2.3). If \(S_R\) is pullback flat and \(r\) is left invertible whenever \(f(r)\) is left invertible for every \(r\in R\), then \(f\) is an effective descent morphism (Corollary 2.4). Every monomorphism of groups is an effective descent morphism (Corollary 2.5). If \(f:R\to R\) is a split monomorphism of \((R,R)\)-biactions, then \(f\) is an effective descent morphism (Theorem 2.6).