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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.