The Nominal/FM Yoneda Lemma

This paper explores versions of the Yoneda Lemma in settings founded upon FM sets. In particular, we explore the lemma for three base categories: the category of nominal sets and equivariant functions; the category of nominal sets and all finitely supported functions, introduced in this paper; and the category of FM sets and finitely supported functions. We make this exploration in ordinary, enriched and internal settings. We also show that the finite support of Yoneda natural transformations is a theorem for free.