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Data fusion as a science has been described in the literature in great detail by many authors, particularly over the last
two decades. These descriptions are, for the vast majority, non-mathematical in nature and have lacked the symbolism
and clarity of mathematical precision. This paper demonstrates a way of describing the science of data fusion using
diagrams and category theory. The description begins using category theory to develop a clear definition of what
fusion is in a mathematical sense. The definitions of fusion rules and fusors show how a notion of ”betterness” can
be defined by developing appropriate functionals. Using a simple diagram of a multisensor process, an explanation
of how receiver operating characteristic (ROC) curves can provide an appropriate functional to compare fusion rules,
fusors, and even classifiers. A partial ordering of a finite number of fusors can then be created.
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