Title: On the Faithfulness of 1-dimensional Topological Quantum Field Theories,
Abstract: This paper explores 1-dimensional topological quantum field theories. We
separately deal with strict and strong 1-dimensional topological quantum field
theories. The strict one is regarded as a symmetric monoidal functor between
the category of 1-cobordisms and the category of matrices, and the strong one
is a symmetric monoidal functor between the category of 1-cobordisms and the
category of finite dimensional vector spaces. It has been proved that both
strict and strong 1-dimensional topological quantum field theories are
faithful.