The Stacks project

Definition 46.3.2. Let $A$ be a ring. A module-valued functor $F$ on $\textit{Alg}_ A$ is called

  1. adequate if there exists a map of $A$-modules $M \to N$ such that $F$ is isomorphic to $\mathop{\mathrm{Ker}}(\underline{M} \to \underline{N})$.

  2. linearly adequate if $F$ is isomorphic to the kernel of a map $\underline{A^{\oplus n}} \to \underline{A^{\oplus m}}$.

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View Definition 46.3.2 as pdf