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nLab: What is precisely the definition of the term homomorphism in the definition of function?

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    • CommentRowNumber1.
    • CommentAuthorMateoC
    • CommentTimeJun 11th 2014
    • (edited Jun 11th 2014)
    In the outstanding definition of function, nLab says: "In a strict sense of the term, a function is a homomorphism f:S→T of sets..."
    1. What is exactly the definition of homomorphism in this context?

    In the definition of homomorphism, nLab says: "More generally, a homomorphism between sets equipped with any algebraic structure is a map preserving this structure."
    2. Then All the sets have an algebraic structure, or a set is an algebraic structure itself?
    • CommentRowNumber2.
    • CommentAuthorZhen Lin
    • CommentTimeJun 11th 2014
    • (edited Jun 11th 2014)

    A set is an algebraic structure in the trivial way: one sort, no operations. The theory of sets is an algebraic theory in the trivial way: no equations.

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