In this field, if a mapping U is left adjoint and creates coequalizers of U-split pairs, it is tripleable by Beck's theorem. The abelian version of its central objects were introduced by Grothendieck's 'Tohoku paper'. Functional programming borrows heavily from this field of mathematics which was invented by Samuel Eilenberg and Saunders Mac Lane. An operation in this field is a monad if it possesses natural transformations. Proofs often involve commutative diagrams, which connect objects with morphisms symbolized by arrows. Homomorphisms between its central objects are functors. For 10 points
In this field, if a mapping U is left adjoint and creates coequalizers of U-split pairs, it is tripleable by Beck's theorem. The abelian version of its central objects were introduced by Grothendieck's 'Tohoku paper'. Functional programming borrows heavily from this field of mathematics which was invented by Samuel Eilenberg and Saunders Mac Lane. An operation in this field is a monad if it possesses natural transformations. Proofs often involve commutative diagrams, which connect objects with morphisms symbolized by arrows. Homomorphisms between its central objects are functors. For 10 points, identify this high-level "abstract nonsense" which links together various branches of mathematics using the namesake entities.
In this field, if a mapping U is left adjoint and creates coequalizers of U-split pairs, it is tripleable by Beck's theorem.