# The Azimuth Project biring

## Definitions

There are two equivalent definitions for birings. Let $\mathsf{CRing}$ denote the category of commutative unital rings and ring homomorphisms.

Definition 1. A biring is a coring object in $(\mathsf{CRing}, \otimes)$.

Definition 2. A biring is a ring $A$ equipped with a lift of the functor $\mathsf{CRing}(A, -) \colon \mathsf{CRing} \to \mathsf{Set}$ through the forgetful functor to a functor $\mathsf{CRing} \to \mathsf{CRing}$.

## References

Birings were introduced in this paper: