hom-set, hom-object, internal hom, exponential object, derived hom-space
loop space object, free loop space object, derived loop space
A function spectrum or mapping spectrum is the analog of a mapping space in the context of stable homotopy theory.
Given two spectra and , their function spectrum is the internal hom in a suitable category of spectra.
In the context of generalized (Eilenberg-Steenrod) cohomology the generalized -cohomology of a topological space is given by the homotopy groups of the mapping spectrum .