We will fix in $M$ a set $\ET$ of morphisms that we want to think of like local isomorphisms. In the examples that we shall consider, these will be either open immersions or étale morphisms. The morphisms of $\ET$ shall be called elementary étalés. We assume that they satisfy the following properties, which are natural given how we think of them, and satisfied by both open immersions and étale morphisms.

1. Every isomorphism is an elementary étalé.
2. The composition of two elementary étalés is an elementary étalé.
3. The elementary étalés are stable under change of base.
4. If both $u\circ v$ and $v$ are elementary étalés, then so is $u$.

In the terminology of Bénabou, $\ET$ is a calibration in $M$.

The elementary étalés are used to make coverings: we will associate to each affine variety $V$ a set of families of elementary étalés over $V$ that are the covers of $V$. We conventionally ask that isomorphisms are covering, and that coverings are stable under change of base and that they have local character.