  In 1992, Kennedy and Tasaki constructed a non-local unitary transformation
that maps between a $\mathbb{Z}_2\times \mathbb{Z}_2$ spontaneously symmetry
breaking phase and the Haldane gap phase, which is a prototypical
Symmetry-Protected Topological phase in modern framework, on an open spin
chain. In this work, we propose a way to define it on a closed chain, by
sacrificing unitarity. The operator realizing such a non-unitary transformation
satisfies non-invertible fusion rule, and implements a generalized gauging of
the $\mathbb{Z}_2\times \mathbb{Z}_2$ global symmetry. These findings connect
the Kennedy-Tasaki transformation to numerous other concepts developed for SPT
phases, and opens a way to construct SPT phases systematically using the
duality mapping.
