some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness.in this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by bernhard banaschewski and walt...

Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by Bernhard Banaschewski and W...

Almost all clean hydrogen that is used in industry made by cogenerating low-cost and other commodities. We propose a framework to make the world's from cogeneration processes.

Any adjunction produces an epireflection in a canonical way, provided there exists a prefactorization system which factorizes all of its unit morphisms through epimorphisms. The stable units property, for the so obtained epireflections, is thereafter equivalently restated in such a manner it is easily recognizable in the examples. Furthermore, having stable units, there is a strong but quite si...

We investigate how to characterize subcategories of abelian categories in terms intrinsic axioms. In particular, we find axioms which generating cogenerating functorially finite subcategories, precluster tilting and cluster categories. As a consequence prove that any d-abelian category is equivalent d-cluster subcategory an category, without assumption on the being projectively generated.

To build replicating systems with new functions, the engineering of existing biological machineries requires a sensible strategy. Protein synthesis Using Recombinant Elements (PURE) system consists of the desired components for transcription, translation, aminoacylation and energy regeneration. PURE might be the basis for a radically alterable, lifelike system after optimization. Here, we regen...