We study the functorial properties of Bridgeland's Hall algebras. Specifically, let A and B be two categories satisfying certain conditions for the definitions of Bridgeland's Hall algebras, and let F : A -> B be a fully faithful exact functor, which preserves projectives, then F induces an embedding of algebras from the Bridgeland's Hall algebra of A to the one of B. In addition, let A be a finite-dimensional algebra over a finite field and B some special quotient algebra of A, then the Bridgeland's Hall algebra of B is the quotient algebra of the one of A. Moreover, we consider the BGP-reflection functors on the category of 2-cyclic complexes and obtain some homomorphisms of algebras among the subalgebras of Bridgeland's Hall algebras.
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