Product (category theory)In , the product of two (or more) in a is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups or rings, and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism to each of the given objects.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
Product topologyIn topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces.
Wilkinson's catalystWilkinson's catalyst is the common name for chloridotris(triphenylphosphine)rhodium(I), a coordination complex of rhodium with the formula [RhCl(PPh3)3], where 'Ph' denotes a phenyl group). It is a red-brown colored solid that is soluble in hydrocarbon solvents such as benzene, and more so in tetrahydrofuran or chlorinated solvents such as dichloromethane. The compound is widely used as a catalyst for hydrogenation of alkenes. It is named after chemist and Nobel laureate Sir Geoffrey Wilkinson, who first popularized its use.
Empty productIn mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity. When numbers are implied, the empty product becomes one. The term empty product is most often used in the above sense when discussing arithmetic operations.
Carbon monoxideCarbon monoxide (chemical formula CO) is a poisonous, flammable gas that is colorless, odorless, tasteless, and slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simplest carbon oxide. In coordination complexes, the carbon monoxide ligand is called carbonyl. It is a key ingredient in many processes in industrial chemistry. The most common source of carbon monoxide is the partial combustion of carbon-containing compounds.
Direct productIn mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the , which formalizes these notions. Examples are the product of sets, groups (described below), rings, and other algebraic structures. The product of topological spaces is another instance. There is also the direct sum – in some areas this is used interchangeably, while in others it is a different concept.
HydrocyanationIn organic chemistry, hydrocyanation is a process for conversion of alkenes to nitriles. The reaction involves the addition of hydrogen cyanide and requires a catalyst. This conversion is conducted on an industrial scale for the production of precursors to nylon. Industrially, hydrocyanation is commonly performed on alkenes catalyzed by nickel complexes of phosphite () ligands. A general reaction is shown: RCH=CH2 + HCN -> RCH2-CH2-CN The reaction involves the addition of and cyanide () to the substrate.
Allotropes of carbonCarbon is capable of forming many allotropes (structurally different forms of the same element) due to its valency. Well-known forms of carbon include diamond and graphite. In recent decades, many more allotropes have been discovered and researched, including ball shapes such as buckminsterfullerene and sheets such as graphene. Larger-scale structures of carbon include nanotubes, nanobuds and nanoribbons. Other unusual forms of carbon exist at very high temperatures or extreme pressures.
EpoxideIn organic chemistry, an epoxide is a cyclic ether, where the ether forms a three-atom ring: two atoms of carbon and one atom of oxygen. This triangular structure has substantial ring strain, making epoxides highly reactive, more so than other ethers. They are produced on a large scale for many applications. In general, low molecular weight epoxides are colourless and nonpolar, and often volatile. A compound containing the epoxide functional group can be called an epoxy, epoxide, oxirane, and ethoxyline.
