Galois and separable extensions of Tambara functors

Abstract

For a map of Tambara functors $R \rightarrow T$ we define when $T$ is separable over $R$ and if $T$ carries an action by some finite group $H$ that fixes $R$ we also define when $T$ is an $H$-Galois extension of Tambara functors. We show that flat and separable extensions are (formally) étale in the sense of Hill and we prove that Galois extensions are separable. We express Nullstellensatzian Tambara functors in the context of Galois theory.