Re: injectivity

Michael Barr mentions the example Ab. There is even an easier reason why tensor products of injectives in Ab are injective and it even injectivity of one factor suffices: Injecitive abelian groups coincide with divisible abelian groups and a tensor product is divisible if one factor is. This holds in a more general sitution, e.g. for modules over a principal ideal domain. It might be worthwile to look for a general (categorical) reason for this phenomenon. Greetings Reinhard Boerger