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.

中文翻译：

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名义上的/FM米田引理

本文探讨了基于 FM 集的设置中的米田引理的版本。特别是，我们探讨了三个基本类别的引理：名义集类别和等变函数；本文介绍的名义集和所有有限支持函数的类别；以及 FM 集和有限支持函数的类别。我们在普通的、丰富的和内部的环境中进行这种探索。我们还表明，米田自然变换的有限支持是免费定理.