additive isomorphism

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• Isomorphism (disambiguation) — Isomorphism may refer to:* Isomorphism, in mathematics, a mapping that preserves the structure * Group isomorphism, in mathematics, a mapping that preserves the group structure * Ring isomorphism, in mathematics, a mapping that preserves both the …   Wikipedia

• Additive category — In mathematics, specifically in category theory, an additive category is a preadditive category C such that any finitely many objects A 1,..., A n of C have a biproduct A 1 ⊕ ⋯ ⊕ A n in C. (Recall that a category C is preadditive if all its… …   Wikipedia

• Isomorphism of categories — In category theory, two categories C and D are isomorphic if there exist functors F : C rarr; D and G : D rarr; C which are mutually inverse to each other, i.e. FG = 1 D (the identity functor on D ) and GF = 1 C . This means that both the objects …   Wikipedia

• Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Formal group — In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were first defined in 1946 by S. Bochner. The term formal group sometimes means the same as formal group law,… …   Wikipedia

• Equivalence of categories — In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are essentially the same . There are numerous examples of categorical equivalences… …   Wikipedia

• Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

• Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

• Finite field — In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and… …   Wikipedia

• Pre-Abelian category — In mathematics, specifically in category theory, a pre Abelian category is an additive category that has all kernels and cokernels.Spelled out in more detail, this means that a category C is pre Abelian if: # C is preadditive, that is enriched… …   Wikipedia