The above findings can be summarized as follows: for a Galois connection, the composite is monotone (being the composite of monotone functions), inflationary, and idempotent. This states that is in fact a closure operator on . Dually, is monotone, deflationary, and idempotent. Such mappings are sometimes called kernel operators. In the context of frames and locales, the composite is called the nucleus induced by . Nuclei induce frame homomorphisms; a subset of a locale is called a sublocale if it is given by a nucleus.