Category theory vs set theory: Mac Lane vs Mathias
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We will discuss some of the differences between category theory and set theory as they are viewed by Mac Lane (category theory) and Mathias (set theory). You can read Mac Lane's paper "Categorical algebra and set-theoretic foundations" as a concise statement of Mac Lane's position. But more interesting is the exchange between Mac Lane and Mathias given it the collection Set theory of the continuum (Judah, Just, Woodin Eds) in the sections "What is Mac Lane missing?" on page 113 and "Is Mathias an Ontologist?" on page 119. All materials can be downloaded in the section "Recommended reading" above.