You can update a document with calculated values using a pipeline like this:

var pipeline = new EmptyPipelineDefinition<C>().Set(x => new { A = x.B });
var result = collection.UpdateMany("{}", pipeline);

But this is not easily discoverable in Intellisense because it depends on the existence of an implicit conversion from PipelineDefinition to UpdateDefinition.

We should add overload(s) to Update that take a PipelineDefinition argument.

This will probably require removing the implicit conversion to avoid ambiguity between overloads, and therefore would be a small breaking change.