Objective Mackey and Tambara functors

Ross Street – 15 May 2024

The first word in the title is intended in the sense that finite sets are objective natural numbers. My main point will be that, at the objective level, the axioms defining abstract Mackey and Tambara functors are categorically familiar. The first step was taken by Harald Lindner in 1976 when he recognized that Mackey functors, defined as pairs of functors, were single functors with domain a category of spans.