The degree structure of Weihrauch-reducibility

We answer a question by Vasco Brattka and Guido Gherardi by proving that the Weihrauch-lattice is not a Brouwer algebra. The computable Weihrauch-lattice is also not a Heyting algebra, but the continuous Weihrauch-lattice is. We further investigate the existence of infinite infima and suprema, as well as embeddings of the Medvedev-degrees into the Weihrauch-degrees.