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

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SESSION 20

Points of an object

Everything that can be said about sets can be expressed in terms of maps and their composition. As we have stressed before, that includes everything about ‘elements’ of sets. We are going to extend this point of view to categories other than that of abstract sets using what we call ‘figures.’ Recall that to specify an element of the set

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for example the element Emilio, we use the following map e from a terminal set 1 to the given set:

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Everything we may want to say about Emilio as an element of this set, we can express ...

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