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For a rosy theory, we give a canonical surjective homomorphism from a Lascar group over A=^eq(A) to a first homology group of a strong type over A, and we describe its kernel by an invariant equivalence relation. As a consequence, we show that the first homology groups of strong types in rosy theories have the cardinalities of one or at least 2^_0. We give two examples of rosy theories having non trivial first homology groups of strong types over ^eq(∅). In these examples, these two homologyarXiv:1504.07721v4 fatcat:yxf5tyy3yjhgbjb4e6wjavb4gm