## 3.3 Classes

Informally we use the notion of a *class*. Given a formula $\phi (x, p_1, \ldots , p_ n)$, we call

a *class*. A class is easier to manipulate than the formula that defines it, but it is not strictly speaking a mathematical object. For example, if $R$ is a ring, then we may consider the class of all $R$-modules (since after all we may translate the sentence “$M$ is an $R$-module” into a formula in set theory, which then defines a class). A *proper class* is a class which is not a set.

In this way we may consider the category of $R$-modules, which is a “big” category—in other words, it has a proper class of objects. Similarly, we may consider the “big” category of schemes, the “big” category of rings, etc.

## 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Your email address will not be published.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 (2)

Comment #1481 by verisimilidude on

Comment #1482 by Johan on