nForum - Discussion Feed (What is precisely the definition of the term homomorphism in the definition of function?) 2022-10-01T06:28:24-04:00 https://nforum.ncatlab.org/ Lussumo Vanilla & Feed Publisher Zhen Lin comments on "What is precisely the definition of the term homomorphism in the definition of function?" (47738) https://nforum.ncatlab.org/discussion/6029/?Focus=47738#Comment_47738 2014-06-11T02:35:25-04:00 2022-10-01T06:28:24-04:00 Zhen Lin https://nforum.ncatlab.org/account/318/ 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.

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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MateoC comments on "What is precisely the definition of the term homomorphism in the definition of function?" (47737) https://nforum.ncatlab.org/discussion/6029/?Focus=47737#Comment_47737 2014-06-11T00:33:13-04:00 2022-10-01T06:28:24-04:00 MateoC https://nforum.ncatlab.org/account/1234/ 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 ... 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? ]]>