Chow-Witt Theory in the Arrowtic Paradigm

In this article we propose a theory of Chow-Witt groups, in the paradigm of Quillen’s arrow based approach to $K$-theory. We refer to this style of arguments as arrowtic paradigm. Other than establishing the machinery needed to work in this paradigm, we establish the homotopy invariance property of the Arrowtic Chow-Witt groups. We also compute the arrowtic Chow-Witt groups of the projective spaces, over fields.