# The Stacks Project

## Tag 0215

Definition 33.4.1. Let $T$ be a scheme. An étale covering of $T$ is a family of morphisms $\{f_i : T_i \to T\}_{i \in I}$ of schemes such that each $f_i$ is étale and such that $T = \bigcup f_i(T_i)$.

The code snippet corresponding to this tag is a part of the file topologies.tex and is located in lines 693–698 (see updates for more information).

\begin{definition}
\label{definition-etale-covering}
Let $T$ be a scheme. An {\it \'etale covering of $T$} is a family
of morphisms $\{f_i : T_i \to T\}_{i \in I}$ of schemes
such that each $f_i$ is \'etale and such that $T = \bigcup f_i(T_i)$.
\end{definition}

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