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.
Dual objectIn , a branch of mathematics, a dual object is an analogue of a dual vector space from linear algebra for in arbitrary . It is only a partial generalization, based upon the categorical properties of duality for finite-dimensional vector spaces. An object admitting a dual is called a dualizable object. In this formalism, infinite-dimensional vector spaces are not dualizable, since the dual vector space V∗ doesn't satisfy the axioms. Often, an object is dualizable only when it satisfies some finiteness or compactness property.
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".
Comma-separated valuesComma-separated values (CSV) is a format that uses commas to separate values. A CSV file stores tabular data (numbers and text) in plain text, where each line of the file typically represents one data record. Each record consists of the same number of fields, and these are separated by commas in the CSV file. If the field delimiter itself may appear within a field, fields can be surrounded with quotation marks . The CSV file format is one type of delimiter-separated file format.
Tab-separated valuesTab-separated values (TSV) is a simple, for storing tabular data. Records are separated by newlines, and values within a record are separated by tab characters. The TSV format is thus a delimiter-separated values format, similar to comma-separated values. TSV is a simple file format that is widely supported, so it is often used in data exchange to move tabular data between different computer programs that support the format. For example, a TSV file might be used to transfer information from a database to a spreadsheet.
