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

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SESSION 32

Subobjects, logic, and truth

1.  Subobjects

We are going to find a remarkable object that connects subobjects, logic, and truth. What should be meant by a ‘subobject,’ or ‘part,’ of an object? Suppose that we have an abstract set X such as

and we look at some of its elements, for example those indicated in the picture

These constitute what can be called a part of the set X. This concept of ‘part’ has two ingredients. First, a part has a shape, which in this example is a set S with precisely two elements,

but there is no meaning in saying ...

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