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Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

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SESSION 29

Binary operations and diagonal arguments

Objects satisfying universal mapping properties are in a sense trivial if you look at them from one side, but not trivial if you look at them from the other side. For example, maps from an object to the terminal object 1 are trivial; but if, after establishing that 1 is a terminal object, one counts the maps whose domain is 1, 1 X, the answer gives us valuable information about X. A similar remark is valid about products. Mapping into a product B1 × B2 is trivial in the sense that the maps X

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