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The coproduct in the category of sets is simply the disjoint union with the maps i j being the inclusion maps.Unlike direct products, coproducts in other categories are not all obviously based on the notion for sets, because unions don't behave well with respect to preserving operations (e.g. the union of two groups need not be a group), and so coproducts in different categories can be ...
The plastic used in plastic shopping bags also started as a by-product of oil refining. [1] By-products are sometimes called co-products to indicate that although they are secondary, they are desired products. For example, hides and leather may be called co-products of beef production. There is no strict distinction between by-products and co ...
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
The limit L of F is called the product of these objects. The cone φ consists of a family of morphisms φ X : L → F(X) called the projections of the product. In the category of sets, for instance, the products are given by Cartesian products and the projections are just the natural projections onto the various factors. Powers.
In a preadditive category, every finitary product is necessarily a coproduct, and hence a biproduct, and conversely every finitary coproduct is necessarily a product (this is a consequence of the definition, not a part of it). The empty product, is a final object and the empty product in the case of an empty diagram, an initial object. Both ...
Pushouts are equivalent to coproducts and coequalizers (if there is an initial object) in the sense that: Coproducts are a pushout from the initial object, and the coequalizer of f, g : X → Y is the pushout of [f, g] and [1 X, 1 X], so if there are pushouts (and an initial object), then there are coequalizers and coproducts;
In this case, B is the kinetic and C is the thermodynamic product of the reaction (see also here). [5] [6] [7] If the reaction is carried out at low temperatures and stopped after a short time, it is spoken of kinetic control, primarily the kinetic product B would be formed. When the reaction is carried out at high temperatures and for long ...
Much of chemistry research is focused on the synthesis and characterization of beneficial products, as well as the detection and removal of undesirable products. Synthetic chemists can be subdivided into research chemists who design new chemicals and pioneer new methods for synthesizing chemicals, as well as process chemists who scale up chemical production and make it safer, more ...