darstellbaren

Darstellbaren is the plural, inflected form of the German adjective darstellbar, meaning capable of being represented, depicted, or rendered. It is used attributively before a plural noun, for example die darstellbaren Objekte, die darstellbaren Funktionen, or die darstellbaren Modelle. The ending -en reflects the standard plural declension after a definite article in German: die darstellbaren Objekte (nominative or accusative plural), den darstellbaren Objekten (dative plural), der darstellbaren Objekte (genitive plural). Thus, darstellbaren appears in all plural cases when the definite article is present.

Linguistically, darstellbar is formed from darstellen, the verb meaning to represent or depict, combined with the suffix -bar, which yields the meaning “able to be.” In common usage, the term covers a broad sense of representability or renderability, from visual depiction to formal representability in mathematical or technical contexts.

In technical and academic German, darstellbar also appears in discussions of representability or renderability within a given formalism. For example, in mathematics or theoretical computer science one speaks of darstellbare Objekte or darstellbare Funktoren, referring to objects or functors that can be represented in a specified way. A typical mathematical statement might define a functor F: C^op → Set to be darstellbar if there exists an object A in C with F ≅ Hom_C(-, A). In English, such usage corresponds to “representable” or “renderable.”

Note that darstellbaren is not a standalone noun; the corresponding noun for the concept of representability is Darstellbarkeit or the related term Darstellung, depending on the exact context. The form darstellbaren thus functions as an adjective in plural phrases rather than as a standalone term.