Final answer:
The Church of San Lorenzo is the name of the church Filippo Brunelleschi built as the parish church for the Medici family. While not directly mentioned in the reference material, San Lorenzo is historically recognized as the Medici's church.
Step-by-step explanation:
The church built by Filippo Brunelleschi, which served as the parish church for the influential Medici family, is known as the Church of San Lorenzo. Although San Lorenzo is not directly mentioned in the provided reference material, historically it is well-documented as the Medici family church. Brunelleschi, a prominent figure in the architecture of the Renaissance, was also famous for constructing the dome of the Cattedrale di Santa Maria del Fiore, commonly known as the Duomo, in Florence. His innovative approach to architecture is renowned for its revival of classicism and the use of linear perspective, which departed from the traditional Gothic style of the period.