Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In abstract algebra, an isomorphism (Greek: isos "equal", and morphe "shape") is a bijective map f such that both f and its inverse f –1 are homomorphisms, i.e., structure-preserving mappings. In the more general setting of category theory, an isomorphism is a morphism f: X -> Y in a category for which there exists an "inverse" f –1: Y -> X, with the property that both...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In abstract algebra, an isomorphism (Greek: isos "equal", and morphe "shape") is a bijective map f such that both f and its inverse f –1 are homomorphisms, i.e., structure-preserving mappings. In the more general setting of category theory, an isomorphism is a morphism f: X -> Y in a category for which there exists an "inverse" f –1: Y -> X, with the property that both f –1f = idX and f f –1 = idY. Informally, an isomorphism is a kind of mapping between objects, which shows a relationship between two properties or operations. If there exists an isomorphism between two structures, we call the two structures isomorphic. In a certain sense, isomorphic structures are structurally identical, if you choose to ignore finer-grained differences that may arise from how they are defined.
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