{* ../../docs_src/path_params_numeric_validations/tutorial003_an_py39.py hl[10] *}

## Number validations: greater than or equal { #number-validations-greater-than-or-equal }

With `Query` and `Path` (and others you'll see later) you can declare number constraints.

Here, with `ge=1`, `item_id` will need to be an integer number "`g`reater than or `e`qual" to `1`.

{* ../../docs_src/path_params_numeric_validations/tutorial004_an_py39.py hl[10] *}

And Pydantic's `Field` returns an instance of `FieldInfo` as well.

`Body` also returns objects of a subclass of `FieldInfo` directly. And there are others you will see later that are subclasses of the `Body` class.

Remember that when you import `Query`, `Path`, and others from `fastapi`, those are actually functions that return special classes.

///

/// tip

You can use **Pydantic models** to declare **query parameters** in **FastAPI**. 😎

/// tip

Spoiler alert: you can also use Pydantic models to declare cookies and headers, but you will read about that later in the tutorial. 🤫

## Dependencies for groups of *path operations* { #dependencies-for-groups-of-path-operations }

    * A "token" is just a string with some content that we can use later to verify this user.
    * Normally, a token is set to expire after some time.
        * So, the user will have to log in again at some point later.
        * And if the token is stolen, the risk is less. It is not like a permanent key that will work forever (in most of the cases).

 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

If you have dependencies with `yield`, the exit code will run *after* the middleware.

If there were any background tasks (covered in the [Background Tasks](background-tasks.md){.internal-link target=_blank} section, you will see it later), they will run *after* all the middleware.

///

## Create a middleware { #create-a-middleware }

To create a middleware you use the decorator `@app.middleware("http")` on top of a function.

{* ../../docs_src/dependencies/tutorial006_an_py39.py hl[11,16] *}

## Dependencies for a group of *path operations* { #dependencies-for-a-group-of-path-operations }

 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

**FastAPI** provides the same `starlette.status` as `fastapi.status` just as a convenience for you, the developer. But it comes directly from Starlette.

///

## Changing the default { #changing-the-default }