We generalize Bj\"{o}rner and Stanley's poset of compositions to m-colored
compositions. Their work draws many analogies between their (1-colored)
composition poset and Young's lattice of partitions, including links to
(quasi-)symmetric functions and representation theory. Here we show that many
of these analogies hold for any number of colors. While many of the proofs for
Bj\"{o}rner and Stanley's poset were simplified by showing isomorphism with the
subword order, we remark that with 2 or more colors, our posets are not
isomorphic to a subword order.Comment: 12 pages, 1 figur