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

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SESSION 4

Division of maps: Isomorphisms

1.  Division of maps versus division of numbers

If composition of maps is analogous to multiplication of numbers, what is the analog of division of numbers? Let’s first review the common features of composition and multiplication. Both operations are associative and have identities. (The identity for multiplication is the number 1.)

Like most analogies this one is only partial because in multiplication of numbers the order doesn’t matter, while in composition of maps it does. If we want both ‘f g’ and ‘ ...

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