OLAP cubeAn OLAP cube is a multi-dimensional array of data. Online analytical processing (OLAP) is a computer-based technique of analyzing data to look for insights. The term cube here refers to a multi-dimensional dataset, which is also sometimes called a hypercube if the number of dimensions is greater than three. A cube can be considered a multi-dimensional generalization of a two- or three-dimensional spreadsheet. For example, a company might wish to summarize financial data by product, by time-period, and by city to compare actual and budget expenses.
Enriched categoryIn , a branch of mathematics, an enriched category generalizes the idea of a by replacing hom-sets with objects from a general . It is motivated by the observation that, in many practical applications, the hom-set often has additional structure that should be respected, e.g., that of being a vector space of morphisms, or a topological space of morphisms. In an enriched category, the set of morphisms (the hom-set) associated with every pair of objects is replaced by an in some fixed monoidal category of "hom-objects".
Category of modulesIn algebra, given a ring R, the category of left modules over R is the whose are all left modules over R and whose morphisms are all module homomorphisms between left R-modules. For example, when R is the ring of integers Z, it is the same thing as the . The category of right modules is defined in a similar way. One can also define the category of bimodules over a ring R but that category is equivalent to the category of left (or right) modules over the enveloping algebra of R (or over the opposite of that).
Category (mathematics)In mathematics, a category (sometimes called an abstract category to distinguish it from a ) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the , whose objects are sets and whose arrows are functions. is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent.
Category of ringsIn mathematics, the category of rings, denoted by Ring, is the whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is , meaning that the class of all rings is proper. The category Ring is a meaning that the objects are sets with additional structure (addition and multiplication) and the morphisms are functions that preserve this structure.
Monoidal categoryIn mathematics, a monoidal category (or tensor category) is a equipped with a bifunctor that is associative up to a natural isomorphism, and an I that is both a left and right identity for ⊗, again up to a natural isomorphism. The associated natural isomorphisms are subject to certain coherence conditions, which ensure that all the relevant s commute. The ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal categories. Monoidal categories can be seen as a generalization of these and other examples.
Product lifecycleIn industry, product lifecycle management (PLM) is the process of managing the entire lifecycle of a product from its inception through the engineering, design and manufacture, as well as the service and disposal of manufactured products. PLM integrates people, data, processes, and business systems and provides a product information backbone for companies and their extended enterprises. The inspiration for the burgeoning business process now known as PLM came from American Motors Corporation (AMC).
Aggregate functionIn database management, an aggregate function or aggregation function is a function where the values of multiple rows are processed together to form a single summary value. Common aggregate functions include: Average (i.e., arithmetic mean) Count Maximum Median Minimum Mode Range Sum Others include: Nanmean (mean ignoring NaN values, also known as "nil" or "null") Stddev Formally, an aggregate function takes as input a set, a multiset (bag), or a list from some input domain I and outputs an element of an output domain O.
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).
Strict 2-categoryIn , a strict 2-category is a with "morphisms between morphisms", that is, where each hom-set itself carries the structure of a category. It can be formally defined as a category over Cat (the , with the structure given by ). The concept of 2-category was first introduced by Charles Ehresmann in his work on enriched categories in 1965. The more general concept of (or weak 2-category), where composition of morphisms is associative only up to a 2-isomorphism, was introduced in 1968 by Jean Bénabou.
Higher category theoryIn mathematics, higher category theory is the part of at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category theory is often applied in algebraic topology (especially in homotopy theory), where one studies algebraic invariants of spaces, such as their fundamental . An ordinary has and morphisms, which are called 1-morphisms in the context of higher category theory.
Database indexA database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and storage space to maintain the index data structure. Indexes are used to quickly locate data without having to search every row in a database table every time said table is accessed. Indexes can be created using one or more columns of a database table, providing the basis for both rapid random lookups and efficient access of ordered records.
