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Representable functors and operations on rings

Idea

This paper gives a definition of biring and plethory, but here the latter are called biring triples. They make connections with Adams operations? and special lambda rings.

Results

Theorem. A functor CRingCRing\mathsf{CRing} \to \mathsf{CRing} is representable if and only iff it has a left adjoint.

Examples

  • The identity functor on CRing\mathsf{CRing} is represented by the ring [x]\mathbb{Z}[x].

  • The functor which sends a ring to its own power series ring is represented by [X 0,X 1,]\mathbb{Z} [X_0, X_1, \dots].