The Stacks project

Remark 35.4.13. Let $f: M \to N$ be a universally injective morphism in $\text{Mod}_ R$. By choosing a splitting $g$ of $C(f)$, we may construct a functorial splitting of $C(1_ P \otimes f)$ for each $P \in \text{Mod}_ R$. Namely, by ( this amounts to splitting $\mathop{\mathrm{Hom}}\nolimits _ R(P, C(f))$ functorially in $P$, and this is achieved by the map $g \circ \bullet $.

Comments (0)

There are also:

  • 4 comment(s) on Section 35.4: Descent for universally injective morphisms

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Your email address will not be published.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.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 08WV. Beware of the difference between the letter 'O' and the digit '0'.