The first two introductory lectures illustrate how
"category logic" is related to AutoLog's indexical forcing.
This short Lecture describes an extended exercise/project involving
natural transformations in categoty theory. The goal here is to design
a lecture providing an AutoLog theory representing the intentions of
relevant category diagrams for Natural Transformations and the related
category logic via AutoLog.
The CategoryLogic is associated with an AutoLog theory
that specifies equality consequences based on term matching
for the indexical literals in a rule as was exemplified in
the Lecture1 and Lecture2.
Here are some online reference articles regarding Natural Transformations
for Category Theory:
We need to formulate natural transformation category logic specifications concerning
covariant and contravarint Functors. Some experimentation with the
rules will be required in order to make the antecedent rule literal Functor
specifications useful. This seemed to be fairly straightforward for Lecture1
and Lecture2, but we do not yet have a satisfying specification for Natural
Transformations. Some difficulty arisess depending on the specific formulations
for the diagrams and the AutoLog logic.
The comments on this page describe lecture goals in a general manner, and readers
are invited to develope thei own versions of detailed design specifications.
We look forward to posting more detailed information for Lecture3 at a later date.
https://ncatlab.org/nlab/show/natural+transformation
https://en.wikipedia.org/wiki/Natural_transformation