The New York City
Category Theory Seminar
April 19th (THURSDAY), 2012. Jean-Pierre Marquis,
Université de Montréal
Title: Categorical Foundations for Mathematics
or how to provide foundations for abstract mathematics
Abstract: In 1977, Sol Feferman presented an argument according to which category theory could not provide a foundation for mathematics. The argument, roughly, suggests that category theory presupposes a notion of collection and a notion of operation and, thus, cannot provide an autonomous foundational framework. In this talk, I examine Feferman's argument and argue that category theory can be seen as a theory of collections and operations and, precisely for that reason, does provide a foundational framework. However, this framework has still to be developed in its technical details, but its overall properties are already fairly clear and lead naturally towards higher dimensional categories.
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