  We introduce frameworks for constructing global derived moduli stacks
associated to a broad range of problems, bridging the gap between the concrete
and abstract conceptions of derived moduli. Our three approaches are via
differential graded Lie algebras, via cosimplicial groups, and via
quasi-comonoids, each more general than the last. Explicit examples of derived
moduli problems addressed here are finite schemes, polarised projective
schemes, torsors, coherent sheaves, and finite group schemes.
