I have some difficulties to figure out what the category of IND-schemes and PRO-schemes are...
Are they full subcategory of algebraic stacks? Are they full subcategory of algebraic spaces?
Edit: I think my question can be misleading, let me clarify it. I know what are ind-object and pro-object. I also know when ind-schemes are actual schemes and when pro-schemes are actual schemes (which is for both, rather rare). My question is: when they are not schemes, are they at least alg. stack or alg. spaces?