Corepresentations of equipped posets over the pair (F;G) are introduced and studied, where F ∈ G is a quadratic field extension. The reduction algorithms and Completion for corepresentations (being in some intuitive sense dual to the known algorithms VII and Completion for representations) are built and investigated, with some applications. The generalized short versions of Differentiations VII and for representations and corepresentations of equipped posets with additional relations are described.

Key words: equipped poset, representation, corepresentation, matrix problem of mixed type, differentiation functor.

Se introducen y estudian corepresentaciones de posets equipados sobre la pareja (F,G), donde F ⊂ G es una extensión cuadrática de campos. Los algoritmos de reducción y Completación para corepresentaciones (que son en algún sentido intuitivo dual a los ya conocidos algoritmos VII y Completación para representaciones) se construyen e investigan, con algunas aplicaciones. Las versiones cortas generalizadas de las Diferenciaciones VII y para representaciones y corepresentaciones de posets equipados con relaciones adicionales se describen.

Palabras clave: poset equipado, representación, núcleo-presentación, problema de la matriz de tipo mixto, diferenciación functor.

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