AutoFixture takes its name from the Fixture pattern:
"a test fixture is all the things we need to have in place in order to run a test and expect a particular outcome. [...] Setting up the test fixture is the first phase of the Four-Phase Test."
While a Shared Fixture is a conceptual possibility, it comes with lots of disadvantages, because it makes it harder to make tests independent of each other.
AutoFixture was explicitly designed to provide a reusable library for creating Fixtures, instead of having to manually code Fixture Objects for every new kind of test context you'd need to create.
There are people who create a single (AutoFixture) Fixture
object and share it across multiple test methods, but I never understood why they do that; it almost defeats the purpose of AutoFixture.
Still, if you find such a set-up useful, who am I to tell you to stop doing it? Whatever floats your boat... However, AutoFixture was designed with the explicit use case of one Fixture
instance per test method in mind, and I haven't seen any advantages to doing it the other way.