Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

X and is the operation on Y . Each type of algebraic structure has its own type of homomorphism. For specific definitions see: group homomorphism r...

Pullback of sieves The most common operation on a sieve is pullback . Pulling back a sieve S on c by an arrow f : c ?? c gives a new sieve f * S on...

Zero morphism - Wikipedia, the free encyclopedia Zero morphism From Wikipedia, the free encyclopedia Jump to: navigation , search In category theor...

In practice, for a valid statement about a particular category , the dual statement is valid in the dual category ( ). [ edit ] Duality The example...

Spectral sequence Abelian category Triangulated category Derived category [ edit ] Applications Group cohomology Galois cohomology Lie algebra coho...

Among other useful concepts are regular epimorphism , extremal epimorphism , strong epimorphism , and split epimorphism . A regular epimorphism coe...

Most authors nowadays simply write algebra instead of abstract algebra . The term abstract algebra now refers to the study of all algebraic structu...

Similarly, in integral calculus , the kernel is the part of the integrand that defines the integral transform ; specifically, the kernel of the ope...

Inspiration, pure and applied mathematics, and aesthetics 4 Notation, language, and rigor 5 Mathematics as science 6 Fields of mathematics 6.1 Quan...

The center of an algebra A consists of all those elements x of A such that xa = ax for all a in A . See also: central simple algebra . The center o...