Objectivist cognition requires that every aspect of category structure be expressible in objectivist terms. In radial categories, no aspect of category is expressible in objectivist terms.
- Lakoff (1987), Pag. 205

Like other categories, a radial category is represented structurally as a container, and its subcategories are containers inside it. What distinguishes it is that it is structured by the CENTER-PERIPHERY schema. One subcategory is the center; the other subcategories are linked to the center by various types of links. Noncentral categories may be “subcenters”, that is, they may have further center-periphery structures imposed on them.
- Lakoff (1987), Pag. 287

The idea of radial category [...] allows us to state otherwise unstateable syntactic generalizations governing the relation of grammatical constructions to one another. [...]. This is done by making use of the concept of ecological location, the location of a construction within a grammatical system. Constructions form radial categories, with a central construction and a number of peripheral constructions linked to the center. Certain generalizations about the details of grammatical constructions can be stated only in terms of where a construction is located in such a radial structure.
- Lakoff (1987), Pag. 291

There is no single representation for a radially structured category. One must provide a representation for the central subcategory and representations for each of the noncentral subcategories, since there are no general principles that can predict the noncentral cases from the central case.
- Lakoff (1987), Pag. 379