One definition of a spectrum is that a spectrum is a sequence <math>E:= _ </math> of CW complexes together with cellular inclusions <math> Sigma E_n to E_ </math>.There are many variations of this definition.
Functions, maps, and morphisms of spectra
There are three natural categories whose objects are spectra, whose morphisms are the functions, or maps, or morphisms defined below.
A function between two spectra E and F is a sequence of maps from E<sub>n</sub> to F<sub>n</sub> that commute with themaps ΣE<sub>n</sub>→E<sub>n+1</sub> and ΣF<sub>n</sub>→F<sub>n+1</sub>.
Given a spectrum <math>E_n</math>, a subspectrum <math>F_n</math> is a sequence of subcomplexes that is also a spectrum. Noting that each i-cell in <math>E_j</math> becomes an (i+1)-cell in <math>E_</math>, a cofinal subspectrum is a subspectrum for which each cell of the parent spectrum is eventually contained in the subspectrum after a finite number of suspensions. Spectra can then be turned into a category by defining a map of spectra... Read More