Differential graded category — In mathematics, especially homological algebra, a differential graded category or DG category for short, is a category whose morphism sets are endowed with the additional structure of a differential graded Z module. In detail, this means that… … Wikipedia
Graded Lie algebra — In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket… … Wikipedia
Graded algebra — In mathematics, in particular abstract algebra, a graded algebra is an algebra over a field (or commutative ring) with an extra piece of structure, known as a gradation (or grading ). Graded rings A graded ring A is a ring that has a direct sum… … Wikipedia
Graded vector space — In mathematics, a graded vector space is a type of vector space that includes the extra structure of gradation, which is a decomposition of the vector space into a direct sum of vector subspaces. Contents 1 N graded vector spaces 2 General I… … Wikipedia
Category of vector spaces — In mathematics, especially category theory, the category K Vect has all vector spaces over a fixed field K as objects and K linear transformations as morphisms. If K is the field of real numbers, then the category is also known as Vec.Since… … Wikipedia
Differential graded algebra — In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded algebra with an added chain complex structure that respects the algebra structure. Contents 1 Definition 2 Examples of DGAs 3 Other facts about … Wikipedia
Homotopy category of chain complexes — In 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 and homotopy equivalences. It lies intermediate between the category of chain… … Wikipedia
Outline of category theory — The following outline is provided as an overview of and guide to category theory: Category theory – area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as… … Wikipedia
List of category theory topics — This is a list of category theory topics, by Wikipedia page. Specific categories *Category of sets **Concrete category *Category of vector spaces **Category of graded vector spaces *Category of finite dimensional Hilbert spaces *Category of sets… … Wikipedia
Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… … Wikipedia
