In the evolutionary literature the term "umbrella theory" can be found. There is no clear definition of that term. When googling the term different meanings not associated with evolutionary theory come up, so I suppose it becomes difficult to give a dictionary definition of a term so widely used with so different meanings. Tis page is solely about the meaning used in evolutionary context.
An umbrella theory of evolutions means a theory that extends evolutionary principles to all fields of natural and social science.
An umbrella theory embraces the evolution of stars and plants, chemical compound, biological organisms, and social structures. Many evolutionary biologists dislike such a broad adaptation of evolutionary principles. Anti-Social-Darwinists in particular fiercely combat any notion of natural selection among human societies. Therefore umbrella theories in evolution have a negative connotation.
This negative connotation is further bolstered by arguments that give the impression that umbrella theories smack of a sweeping generalization or false analogy fallacy. However, those fallacies are only committed if the abstraction proviso is neglected.
Fauceir theory may be called an umbrella theory, but I would rather prefer the term atomic or analytic theory. Fauceir theory is in sharp contrast with typical evolutionary umbrella theories. While umbrella theories try to generalize natural laws to embrace ever more objects of the real world, fauceir theory goes into the opposite directs. Fauceir theory brakes down real objects into functional units that resemble each other in a wide range of real objects. While by umbrella theories the outline of the real object blurs which makes it nearly impossible to develop precise predictions, fauceir theory allows to construct sharp models of real objects, even if objects differ widely.
In that aspect fauceir theory is similar to the atomic theory that describes the properties of chemical compounds by its content of atoms.