Born in Milan, early in his youth he started studying fine arts under the tutelage of Stefano Bersani. In 1906 he joined the noted Brera Academy, where he met some of the most renowned Italian painters of the epoch, including Giuseppe Mentessi, Carlo Cattaneo, Cesare Tallone, as well as Achille Funi, Emilio Gola and Carlo Carrà. The following year he appeared at the Brera art exhibition, which was followed by his appearance at the 1912 Venice Biennale. Since then he participated in every Venetian Biennale excepting those held in 1940, 1950 and 1952.
Drafted into the Italian Army in 1915, he served at various fronts of the Great War. In 1917 he married Maria Arpesani. In the 1920s, Carpi developed the style of his paintings and landscapes under the influence of Italian 19th-century painters. For his works in 1925 he was awarded with the prestigious Premio Principe Umberto. In 1927 he became the author of new frescoes in the San Simpliciano Basilica in Milan. In 1930 he became the professor and deacon of the faculty of painting at his alma mater. In 1934 he also prepared a project for the new stained glass windows in the famous Duomo of Milan, which however was not completed until after the World War II. In 1937 he appeared at the Exposition Internationale des Arts et Techniques dans la Vie Moderne in Paris, where he was awarded a bronze medal.
In January 1944, during the World War II, he was arrested after a colleague informed on him, and was imprisoned in the concentration camp Gusen I of the Mauthausen-Gusen system, where he kept a diary and made a number of sketches portraying life and death in the camp. Liberated at the end of the war, he returned to Milan, where in 1956 he was awarded the state prize for his works and cultural merits. He also became the rector of his alma mater. In 1972 he prepared one of his last major works, a large monographic exhibition of his works.
He died in 1973 in Milan.
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