Mario Román


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Tambara module

Last updated Nov 27, 2022

Definition. Let $(𝔸, ⊗, I)$ be a monoidal category. A Tambara module is a profunctor $T ﹕ 𝔸^{op} × 𝔸 → \mathbf{Set}$ endowed with transformations $$t_l^M \colon T(X;Y) → T(M ⊗ X, M ⊗ Y),$$ $$t_r^M \colon T(X;Y) → T(X ⊗ M, Y ⊗ M),$$ that are natural in both $X$ and $Y$, but also dinatural on $M$. These must moreover satisfy the following axioms: