The Category of Maximal Cohen–Macaulay Modules as a Ring with Several Objects

Category of Polygroup Objects

The category of generalized crossed modules

In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...

category of polygroup objects

Ring With All Finitely Generated Modules Retractable

Modules as Objects in Newspeak

We describe support for modularity in Newspeak, a programming language descended from Smalltalk [33] and Self [68]. Like Self, all computation — even an object’s own access to its internal structure — is performed by invoking methods on objects. However, like Smalltalk, Newspeak is class-based. Classes can be nested arbitrarily, as in Beta [44]. Since all names denote method invocations, all cl...