A uni-molecular chemical reaction is defined by the natural transformations
specified in the following commutative diagram:
![]() |
(0.1) |
with the states of molecular sets
and
being defined as the endomorphism sets
and
, respectively. In general, molecular sets
are defined as finite sets whose elements are molecules; the molecules are mathematically defined in terms of their molecular observables
as specified next. In order to define molecular observables one needs to define first the concept
of a molecular class variable
or
.
A molecular class variables is defined as a family of molecular sets
, with
being either an indexing set, or a proper class, that defines the variation range of the
.
Most physical, chemical or biochemical applications require that
is restricted to a finite set, (that is, without any sub-classes). A morphism, or molecular mapping,
of molecular sets, with
being real time values, is defined as a time-dependent mapping or function
also called a molecular transformation,
.
An
observable of
, characterizing the products of chemical type
“B” of a chemical reaction is defined as a morphism:
where
![]() |
(0.2) |
With these concepts and preliminary data one can now define the category of molecular sets and their transformations as follows.
Classification: AMS MSC: 18D35 (category theory; homological algebra :: categories with structure :: Structured objects in a category ) 92B05 (Biology and other natural sciences :: Mathematical biology in general :: General biology and biomathematics) 18E05 (Category theory; homological algebra :: abelian categories :: Preadditive, additive categories) 81-00 (quantum theory :: General reference works )
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