The purpose of the book is to advance in the understanding of
brain function by defining a general framework for representation
based on category theory. The idea is to bring this mathematical
formalism into the domain of neural representation of physical
spaces, setting the basis for a theory of mental representation,
able to relate empirical findings, uniting them into a sound
theoretical corpus.
The innovative approach presented in the book provides a horizon
of interdisciplinary collaboration that aims to set up a common
agenda that synthesizes mathematical formalization and empirical
procedures in a systemic way. Category theory has been successfully
applied to qualitative analysis, mainly in theoretical computer
science to deal with programming language semantics. Nevertheless,
the potential of category theoretic tools for quantitative analysis
of networks has not been tackled so far. Statistical methods to
investigate graph structure typically rely on network parameters.
Category theory can be seen as an abstraction of graph theory.
Thus, new categorical properties can be added into network analysis
and graph theoretic constructs can be accordingly extended in more
fundamental basis. By generalizing networks using category theory
we can address questions and elaborate answers in a more
fundamental way without waiving graph theoretic tools. The vital
issue is to establish a new framework for quantitative analysis of
networks using the theory of categories, in which computational
neuroscientists and network theorists may tackle in more efficient
ways the dynamics of brain cognitive networks.
The intended audience of the book is researchers who wish to
explore the validity of mathematical principles in the
understanding of cognitive systems. All the actors in cognitive
science: philosophers, engineers, neurobiologists, cognitive
psychologists, computer scientists etc. are akin to discover along
its pages new unforeseen connections through the development of
concepts and formal theories described in the book. Practitioners
of both pure and applied mathematics e.g., network theorists, will
be delighted with the mapping of abstract mathematical concepts in
the terra incognita of cognition.
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