Meanings, metaphors, and morphisms: Theory of indeterminate natural transformation (TINT)

Miho Fuyama, Hayato Saigo

Research output: Contribution to journalArticlepeer-review


In the present paper, we propose a new theory named "Theory of indeterminate natural transformation (TINT)" to investigate the dynamical creation of meanings as association relationships between images, focusing on the metaphor comprehension as an example. TINT models the meaning creation as a kind of stochastic processes based on the mathematical structure defined by association relationships as mor-phisms in category theory, so as to represent the indeterminate nature of structure-structure interactions between the systems of the meanings of images. Such interactions are formulated in terms of so-called coslice categories and functors as structure-preserving correspondence between them. The relationship between such functors is "indeterminate natural transformation", the central notion in TINT, which models the creation of meanings in a precise manner. For instance, the process of metaphor comprehension is modeled by the construction of indeterminate natural transformation from a canonically defined functor which we call the base-of-metaphor functor.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Jan 31
Externally publishedYes


  • Category theory
  • Indeterminate Natural Transformation
  • Meaning
  • Meaning
  • Metaphor
  • Metaphor
  • Morphism
  • Semantic space

ASJC Scopus subject areas

  • General

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