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

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ARTICLE II

Isomorphisms

Retractions, sections, idempotents, automorphisms

1.  Isomorphisms

It seems probable that before man learned to count, it was first necessary to notice that sometimes one collection of things has a certain kind of resemblance to another collection. For example, these two collections

are similar. In what way? (Remember that numbers had not yet been invented, so it is not fair to say ‘the resemblance is that each has three elements.’)

After some thought, you may arrive at the conclusion that the resemblance is actually given ...

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