  We give an explicit description of factorization algebras over the affine
line, constructing them from the gluing data determined by its corresponding
OPE algebra. We then generalize this construction to factorization monoids,
obtaining a description of them in terms of a non-linear version of OPE
algebras which we call OPE monoids. In the translation equivariant setting this
approach allows us to define vertex ind-schemes, which we interpret as a
conformal analogue of the notion of Lie group, since we show that their
linearizations yield vertex algebras and that their Zariski tangent spaces are
Lie conformal algebras.
