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An additive category is a category for which the morphism sets have the structure of Abelian groups. It satisfies some, but not all the properties of an Abelian category.

A number which can be represented both in the form x_0^2-Dy_0^2 and in the form Dx_1^2-y_1^2. This is only possible when the Pell equation x^2-Dy^2=-1 (1) is solvable. Then ...

Define O = lim_(->)O(n),F=R (1) U = lim_(->)U(n),F=C (2) Sp = lim_(->)Sp(n),F=H. (3) Then Omega^2BU = BU×Z (4) Omega^4BO = BSp×Z (5) Omega^4BSp = BO×Z. (6)

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

The branch of mathematics which formalizes a number of algebraic properties of collections of transformations between mathematical objects (such as binary relations, groups, ...

The average of the values of the class limits for a given class. A class mark is also called a midvalue or central value (Kenney and Keeping 1962, p. 14), and is commonly ...

The classification of a collection of objects generally means that a list has been constructed with exactly one member from each isomorphism type among the objects, and that ...

A diminished polyhedron is a polyhedron in which one or more groups of associated faces (such as those comprising the top of a pyramid or cupola in the case of a Johnson ...

A morphism f:Y->X in a category is an epimorphism if, for any two morphisms u,v:X->Z, uf=vf implies u=v. In the categories of sets, groups, modules, etc., an epimorphism is ...

A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their automorphism groups.