A Pedestrian Guide to Topos Theory

For a while now I’ve been slowly working on trying to figure out how to develop a more accessible introduction to an area of mathematics called topos theory.

Topos theory has lots of interesting connections to other areas of mathematics and related topics, including logic, geometry, topology (the study of spaces), and computer science. Amongst its many applications, topos theory offers: a logic for reasoning about situations that don’t involve sharp clear distinctions and yes/no questions; a formulation of calculus that justifies the naive approach we first learned in school; a language in which quantum mechanics looks less weird; and even a different way of understanding the foundations of mathematics itself.

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