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

A

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