The Stacks project

Definition 8.6.1. Let $\mathcal{C}$ be a site.

  1. A stack in setoids over $\mathcal{C}$ is a stack over $\mathcal{C}$ all of whose fibre categories are setoids.

  2. A stack in sets, or a stack in discrete categories is a stack over $\mathcal{C}$ all of whose fibre categories are discrete.

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View Definition 8.6.1 as pdf