Additive category information

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

additive category for preadditive categories, but here we follow the current trend of reserving this term for certain special preadditive categories (see...

In Def. 1.2.6, it is required that an additive category have a zero object (empty biproduct). An additive category is preabelian if every morphism has both...

addition operation Additive set-function see Sigma additivity Additive category, a preadditive category with finite biproducts Additive inverse, an arithmetic...

preadditive category (or additive category, or abelian category), then D may be turned into a preadditive category (or additive category, or abelian category) in...

full subcategory of Grp. Ab is an abelian category, but Grp is not. Indeed, Grp isn't even an additive category, because there is no natural way to define...

homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies...

the quotient category C/~ will also be additive, and the quotient functor C → C/~ will be an additive functor. The concept of an additive congruence relation...

Cokernel Pushout (category theory) Direct limit Biproduct Direct sum Preadditive category Additive category Pre-Abelian category Abelian category Exact sequence...

v}}Z{\xrightarrow {{} \atop w}}} for short. A triangulated category is an additive category D with a translation functor and a class of triangles, called...

necessary for the usual definition of such a sequence. An exact category E is an additive category possessing a class E of "short exact sequences": triples of...

cholesterol, fat, or sodium. To support to the creation of tapioca pearls, some additives are used, especially during the tapioca flour making process. Sulfuric...

necessarily real), either as additive mathematical elements of a color space or as irreducible phenomenological categories in domains such as psychology...

the category, one requires d ( id A ) = 0 {\displaystyle d(\operatorname {id} _{A})=0} . Any additive category may be considered to be a DG-category by...

{A}}} , the functor category Add ⁡ ( C , A ) {\displaystyle \operatorname {Add} ({\mathcal {C}},{\mathcal {A}})} of all additive covariant functors from...

think, therefore I am" Sum certain, a legal term Addition Additive category Preadditive category This disambiguation page lists articles associated with...

if G is additive with a left adjoint F, then F is also additive. Moreover, if both C and D are additive categories (i.e. preadditive categories with all...

An additive category is a preadditive category in which all finite biproducts exist. In particular, biproducts always exist in abelian categories. Borceux...

that can still be controlled. Let P and Q be abelian categories, and let F: P→Q be a covariant additive functor (so that, in particular, F(0) = 0). We say...

homotopy category of genuine G-spectra spanned by the suspension spectra of finite G-sets. The Burnside category is self-dual. If C is an additive category, then...

Food additives are substances added to food to preserve flavor or enhance taste, appearance, or other sensory qualities. Some additives have been used...

(like all food additives) must be included in the list of ingredients of a food product with its additive category and listed name or additive number, that...

In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused...

preadditive category, and because the direct sum of finitely many abelian groups yields a biproduct, we indeed have an additive category. In Ab, the notion...

Grothendieck group of an exact category A {\displaystyle {\mathcal {A}}} . Simply put, an exact category is an additive category together with a class of distinguished...

Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

spaces and Hilbert spaces. An additive category is an abstraction of the properties of the category of modules. In such a category, finite products and coproducts...