Cell Language Theory, The: Connecting Mind And Matter

12 The Cell Language Theory: Connecting Mind and Matter

b2861 The Cell Language Theory: Connecting Mind and Matter “6x9”

2.1.1 What Is a Functor?

Spivak [31] defines a “functor” as follows:

Different branches of mathematics (or human knowledge; my addition)

can be formalized into categories. These categories can then be

connected together by functors. And the sense in which these functors

provide powerful communication of ideas is that facts and theorems

(regularities; my addition) proven in one category (discipline; my

addition) can be transferred through a connecting functor to yield

proofs of analogous theorems in another category. A functor is like a

conductor of mathematical truth.

2.1.2 The Ur-Category

A category can be understood as a set of at least three objects that are

related to each other in such a manner that the properties explained in the

legend to Figure 2.1 hold. For the convenience of typing with a computer

keyboard, the usual triangular figure for a category, i.e., Figure 2.1, is

transformed into a square network as shown in Figure 2.2 with the mean­

ings of the symbols unchanged. That is, Figure 2.2 is equivalent to or

synonymous with Figure 2.1, the difference being that the linear arrow h

in Figure 2.1 is converted into a U­shaped arrow in Figure 2.2.

Figures 2.1 and 2.2 will be referred to as the ur-category defined as

the simplest category to which all more complex categories can be

A

fg

BC

h

Figure 2.1 A diagrammatic representation of a category. Adapted from [32]. The nodes,

A, B, and C are the objects belonging to a category and the arrows f, g, and h are the rules

of mapping (also called “structure­preserving mappings”) from one node to another such

that f followed by g leads to the same result as h, which is denoted as g ° f = h. When this

condition is met, the triangle is said to commute, and the figure is referred to as a

“commutative triangle”.

(2.3)

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