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Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
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products in a category without reference to objects or sources and targets
As Freyd and Scedrov show in "Categories, Allegories", you can think of a category as some kind of partial monoid. Such a monoid has a set of partial units that take over the role of objects in standa …