Additive categoryIn mathematics, specifically in , an additive category is a C admitting all finitary biproducts. There are two equivalent definitions of an additive category: One as a category equipped with additional structure, and another as a category equipped with no extra structure but whose objects and morphisms satisfy certain equations. A category C is preadditive if all its hom-sets are abelian groups and composition of morphisms is bilinear; in other words, C is over the of abelian groups.
Preadditive categoryIn mathematics, specifically in , a preadditive category is another name for an Ab-category, i.e., a that is over the , Ab. That is, an Ab-category C is a such that every hom-set Hom(A,B) in C has the structure of an abelian group, and composition of morphisms is bilinear, in the sense that composition of morphisms distributes over the group operation. In formulas: and where + is the group operation. Some authors have used the term additive category for preadditive categories, but here we follow the current trend of reserving this term for certain special preadditive categories (see below).
CoproductIn , the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism. It is the category-theoretic to the , which means the definition is the same as the product but with all arrows reversed.
ColumnA column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term column applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a post.
Mid-ocean ridgeA mid-ocean ridge (MOR) is a seafloor mountain system formed by plate tectonics. It typically has a depth of about and rises about above the deepest portion of an ocean basin. This feature is where seafloor spreading takes place along a divergent plate boundary. The rate of seafloor spreading determines the morphology of the crest of the mid-ocean ridge and its width in an ocean basin. The production of new seafloor and oceanic lithosphere results from mantle upwelling in response to plate separation.
Solomonic columnThe Solomonic column, also called Barley-sugar column, is a helical column, characterized by a spiraling twisting shaft like a corkscrew. It is not associated with a specific classical order, although most examples have Corinthian or Composite capitals. But it may be crowned with any design, for example, making a Roman Doric solomonic or Ionic solomonic column.
