This theory encodes the idea of "efficiency" in the universal properties of free objects, which usually involve a triangular diagram in which their natural transformations commute.
This theory led to the formulation of mathematical "topoi," which behave like sheaves and give rise to a semantics of modal logic usually named for André Joyal and Saul Kripke. In this theory, a result that closely resembles Cayley's Theorem from group theory, fully describes the transformations on a "representable" class of objects, and is named for Yoneda. This theory was studied in terms of a hyphenated "onto-logy" and the concept of "being-there" in a book about the "Transcendental" by Alain (*) Badiou. This theory encodes the idea of "efficiency" in the universal properties of free objects, which usually involve a triangular diagram in which their natural transformations commute. This theory gave rise to the computer science terms "covariant" and "contravariant." Saunders Mac Lane introduced this theory's language of morphisms, arrows, and functors. For 10 points, name this generalization of much of algebra and set theory, so general that it was attacked as "abstract nonsense.
This theory led to the formulation of mathematical "topoi," which behave like sheaves and give rise to a semantics of modal logic usually named for André Joyal and Saul Kripke.
category theory [prompt on any answer involving "algebra"; prompt on "mathematics" or similar, e.g. "Mathematics of the Transcendental"]