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We prove that affine functors are equal to a direct limit of affine schemes and that affine schemes, formal schemes, the completion of affine schemes along a closed subscheme, etc., are affine functors.\n  Endowing an affine functor $\\mathbb X$ with a functor of monoids structure is equivalent to endowing $\\mathbb A_{\\mathbb X}$ with a functor of bialgebras structure. 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