The Labor Theory of Value - What Is Your Property?

In capitalism, many people are being brought together. They are doing individual, little parts of the total necessary labor, but not every part. The division of labor inside a factory means that no one person can point to the nished shoe and say, that's mine. In this sense, it was his or her personal property. Not even a marxist has a problem with that kind of personal property. And this really chapped markis hide. Now is any of this true? Is this really how works? Is it everything correct?"