Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.

A straightforward formulation of a mathematical problem is mostly not adequate for resolution theorem proving. We present a method to optimize such formulations by exploiting the variability of rst-order logic. The optimizing transformation is described as logic morphisms, whose operationalizations are tactics. The diierent behaviour of a resolution theorem prover for the source and target form...

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...

Contents 1. Introduction 1 2. Conventions 2 3. Unramified morphisms 2 4. Three other characterizations of unramified morphisms 4 5. The functorial characterization of unramified morphisms 5 6. Topological properties of unramified morphisms 6 7. Universally injective, unramified morphisms 7 8. Examples of unramified morphisms 9 9. Flat morphisms 10 10. Topological properties of flat morphisms 11...

Contents 1. Introduction 1 2. Conventions 2 3. Unramified morphisms 2 4. Three other characterizations of unramified morphisms 4 5. The functorial characterization of unramified morphisms 5 6. Topological properties of unramified morphisms 6 7. Universally injective, unramified morphisms 7 8. Examples of unramified morphisms 9 9. Flat morphisms 10 10. Topological properties of flat morphisms 11...

We show that morphisms from n A∞-algebras to a single one are maps over an operad module with n+ 1 commuting actions of the operad A∞, whose algebras are conventional A∞-algebras. The composition of A∞-morphisms with several entries is presented as a convolution of a coalgebra-like and an algebra-like structures. Under these notions lie two examples of Cat-operads: that of graded modules and of...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...