In many references, 'Toen, Highera nd derived stacks:a global overview', 'Toen-Vezzosi, Homotopical algebraic geometry II',... the definition of n-geometric stack appears.

In 'Not' derived case, the definition starts at declaring affine schemes as a (-1)-geometric stacks and inductively defines n-geometric stacks by some procedure.

Toen-Vezzosi, HAG II, Remark 2.1.1.5 says that algebraic spaces and schemes are automatically 1-geometric stacks. I can check that schemes are 1-geometric(It does not depend on whether a scheme is separated or not). But I can't check it easily that algebraic spaces are 1-geometric stacks.

In many references (Toen, Higher and derived stacks: a global overview, Toen, Vezzosi, Homotopical algebraic geometry II, and so on), the definition of $n$-geometric stack appears.

In the non-derived case, the definition starts by declaring affine schemes as $(-1)$-geometric stacks and inductively defines $n$-geometric stacks by some procedure.

Toen-Vezzosi, HAG II, Remark 2.1.1.5 says that algebraic spaces and schemes are automatically 1-geometric stacks. I can check that schemes are 1-geometric. (It does not depend on whether a scheme is separated or not.) But I can't check easily that algebraic spaces are 1-geometric stacks.

In many references, 'Toen, Highera nd derived stacks:a global overview', 'Toen-Vezzosi, Homotopical algebraic geometry II',... the definition of n-geometric stack appears.

In 'Not' derived case, the definition starts at declaring affine schemes as a (-1)-geometric stacks and inductively defines n-geometric stacks by some procedure.

Toen-Vezzosi, HAG II, Remark 2.1.1.5 says that algebraic spaces and schemes are automatically 1-geometric stacks. I can check that schemes are 1-geometric(It does not depend on whether a scheme is separated or not). But I can't check it easily that

In many references, 'Toen, Highera nd derived stacks:a global overview', 'Toen-Vezzosi, Homotopical algebraic geometry II',... the definition of n-geometric stack appears.

In 'Not' derived case, the definition starts at declaring affine schemes as a (-1)-geometric stacks and inductively defines n-geometric stacks by some procedure.

Toen-Vezzosi, HAG II, Remark 2.1.1.5 says that algebraic spaces and schemes are automatically 1-geometric stacks. I can check that schemes are 1-geometric(It does not depend on whether a scheme is separated or not). But I can't check it easily that algebraic spaces are 1-geometric stacks.