  The affine Kauffmann category is a strict monoidal category and can be
considered as a $q$-analogue of the affine Brauer category in (Rui et al. in
Math. Zeit. 293, 503-550, 2019). In this paper, we prove a basis theorem for
the morphism spaces in the affine Kauffmann category. The cyclotomic Kauffmann
category is a quotient category of the affine Kauffmann category. We also prove
that any morphism space in this category is free over an integral domain
$\mathbb K$ with maximal rank if and only if the $\mathbf u$-admissible
condition holds in the sense of Definition 1.13.
