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

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SESSION 1

Galileo and multiplication of objects

1.  Introduction

Our goal in this book is to explore the consequences of a new and fundamental insight about the nature of mathematics which has led to better methods for understanding and using mathematical concepts. While the insight and methods are simple, they are not as familiar as they should be; they will require some effort to master, but you will be rewarded with a clarity of understanding that will be helpful in unravelling the mathematical aspect of any subject matter.

The basic notion which underlies all the others is that of a category, a ‘mathematical universe’. There are many categories, each appropriate to a particular subject matter, and there are ways to pass from one category ...

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