Using familiar constructions on the category of monoids, a fully abstract model of Basic SCI is constructed. Basic SCI is a version of Reynolds’s higher-order imperative programming language Idealized Algol, restricted by means of a linear type system so that distinct identifiers are never aliases. The model given here is concretely the same as Reddy’s object spaces model, so this work also shows that Reddy’s model is fully abstract, which was not previously known.