Lemma 39.18.3. The notions of restricting groupoids and (pre-)equivalence relations defined in Definitions 39.18.2 and 39.3.3 agree via the constructions of Lemmas 39.13.2 and 39.13.3.

**Proof.**
What we are saying here is that $R'$ of Lemma 39.18.1 is also equal to

\[ R' = (U' \times _ S U')\times _{U \times _ S U} R \longrightarrow U' \times _ S U' \]

In fact this might have been a clearer way to state that lemma. $\square$

## Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)