Ind-scheme

In algebraic geometry, an ind-scheme is a set-valued functor that can be written (represented) as a direct limit (i.e., inductive limit) of closed embedding of schemes.

• ${\displaystyle \mathbb {C} P^{\infty }=\varinjlim \mathbb {C} P^{N}}$ is an ind-scheme.
• Perhaps the most famous example of an ind-scheme is an infinite grassmannian (which is a quotient of the loop group of an algebraic group G.)