An exact sequence is a mathematical concept used in algebraic topology and homological algebra. It consists of a sequence of objects and morphisms (arrows) between them, where the image of one morphism is equal to the kernel of the next. This property ensures that the sequence captures important relationships between the objects involved, often revealing structural information.
In an exact sequence, if you have a sequence of groups or modules, it indicates that the elements are related in a specific way. For example, in a sequence involving groups, the exactness at a group means that every element in the image of one group is also an element of the next group's kernel.