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What is category theory to cognitive science? Compositional representation and comparison
1Mathematical Neuroscience Group, Human Informatics and Interaction Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan.
Category theory offers a formal framework for understanding cognitive science. This approach equates category theory concepts like functors and natural transformations to cognitive processes such as representation and comparison, enhancing accessibility for researchers.
Area of Science:
- Cognitive Science
- Theoretical Computer Science
- Philosophy of Mind
Background:
- Category theory and cognitive science both explore structural relations.
- Cognitive science traditionally lacks formal mathematical frameworks for structural analysis.
- Category theory provides a powerful language for abstract structures.
Purpose of the Study:
- To bridge the gap between category theory and cognitive science.
- To propose a novel framework for understanding cognition using category theory.
- To make category theory accessible and informative for cognitive scientists.
Main Methods:
- Conceptual analysis linking category theory concepts to cognitive processes.
- Development of an analogy: "Category theory is to cognitive science as functor is to representation; as natural transformation is to comparison."
- Literature review of both fields to identify common structural principles.
Main Results:
- Category theory offers a formal, structural approach to cognition.
- Functors can model cognitive representation.
- Natural transformations can model cognitive comparison and change.
Conclusions:
- Category theory provides a valuable, yet underutilized, toolset for cognitive science.
- The proposed slogan enhances understanding of category theory's relevance to cognition.
- Adopting category theory can lead to new insights into the structure of the mind.
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