A pigeon, a nest, a baby bird?

For the last couple of weeks, we’ve had a pigeon nesting on one of the pipes coming down from our roof. She sits there for most of the day, so I assume she’s incubating some eggs. Once in a while she flies away and we see her with another pigeon (her mate?). The kids are enthralled, we can’t wait for the baby birds to be born – I hope we see them.