Product (category theory) — In category theory, the product of two (or more) objects in a category 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, the direct… … Wikipedia
Product category — In the mathematical field of category theory, the product of two categories C and D , denoted nowrap| C × D and called a product category, is a straightforward extension of the concept of the Cartesian product of two sets.DefinitionThe product… … Wikipedia
Product topology — In 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 obvious,… … Wikipedia
Product order — In mathematics, given two ordered sets A and B, one can induce a partial ordering on the Cartesian product A × B. Given two pairs (a1,b1) and (a2,b2) in A × B, one sets (a1,b1) ≤ (a2,b2) if and only if a1 ≤ a2 and b1 ≤ b2. This ordering is called … Wikipedia
Categorical algebra — In category theory, a field of mathematics, a categorical algebra is an associative algebra, defined for any locally finite category and commutative ring with unity.It generalizes the notions of group algebra and incidence algebra,just as… … Wikipedia
Empty product — In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is equal to the multiplicative identity 1, given that it exists for the multiplication operation in question, just as the empty sum the result of… … Wikipedia
Direct product — In mathematics, one can often define a direct product of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one… … Wikipedia
Tensor product of graphs — In graph theory, the tensor product G × H of graphs G and H is a graph such that * the vertex set of G × H is the Cartesian product V(G) × V(H) ; and * any two vertices (u,u ) and (v,v ) are adjacent in G × H if and only if u is adjacent with v… … Wikipedia
Cartesian product — Cartesian square redirects here. For Cartesian squares in category theory, see Cartesian square (category theory). In mathematics, a Cartesian product (or product set) is a construction to build a new set out of a number of given sets. Each… … Wikipedia
Universal property — In various branches of mathematics, certain constructions are frequently defined or characterised by an abstract property which requires the existence of a unique morphism under certain conditions. These properties are called universal properties … Wikipedia
