A functional analytic perspective to the div-curl Lemma

We present an abstract functional analytic formulation of the celebrated div-curl lemma found by F. Murat and L. Tartar. The viewpoint in this note relies on sequences for operators in Hilbert spaces. Hence, we draw the functional analytic relation of the div-curl lemma to differential forms and other sequences such as the Grad grad-sequence discovered recently by D. Pauly and W. Zulehner in connection with the biharmonic operator.