Algebra and Coalgebra Objects in Categories, and Functors Having Adjoints

2015 ◽  
pp. 457-530
Author(s):  
George M. Bergman
Keyword(s):  
Categories And Functors

scholarly journals A Category Theoretic Approach to Metaphor Comprehension: Theory of Indeterminate Natural Transformation

2020 ◽  
Author(s):  
Miho Fuyama ◽  
Hayato Saigo ◽  
Tatsuji Takahashi
Keyword(s):  
Category Theory ◽  
Natural Transformation ◽  
Mathematical Structure ◽  
Theoretic Approach ◽  
Metaphor Comprehension ◽  
Central Notion ◽  
Meaning Creation ◽  
Natural Transformations ◽  
Categories And Functors ◽  
The Relationship

We propose the theory of indeterminate natural transformation (TINT) to investigate the dynamical creation of meaning as an association relationship between images, focusing on metaphor comprehension as an example. TINT models meaning creation as a type of stochastic process based on mathematical structure and defined by association relationships, such as morphisms in category theory, to represent the indeterminate nature of structure-structure interactions between the systems of image meanings. Such interactions are formulated in terms of the so-called coslice categories and functors as structure-preserving correspondences 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, metaphor comprehension is modeled by the construction of indeterminate natural transformations from a canonically defined functor, which we call the base-of-metaphor functor.

Categories and Functors

Algebra II ◽  
2017 ◽  
pp. 187-226
Author(s):  
Alexey L. Gorodentsev
Keyword(s):  
Categories And Functors

The trichotomic machine

Semiotica ◽  
2019 ◽  
Vol 2019 (228) ◽  
pp. 173-192 ◽  
Author(s):  
Robert Marty
Keyword(s):  
Formal Analysis ◽  
Homological Algebra ◽  
Algebraic Theory ◽  
Hierarchical Structures ◽  
Additional Benefit ◽  
General Methodology ◽  
New Methodologies ◽  
Basic Concepts ◽  
Categories And Functors

AbstractThe formal analysis of the principles leading the classification of the hexadic, decadic, and triadic signs from C. S. Peirce especially, gives rise to a general methodology allowing to systematically classify any n-adic combinatory named “protosign.” Basic concepts of the algebraic theory regarding the categories and functors will be used. That formalization provides an additional benefit by highlighting and systematizing formal immanent relationships between the classes of protosigns (or signs). Well known hierarchical structures (lattices) are then obtained. Thanks to the contribution of specific concepts in the Homological Algebra, new methodologies of analysis and creation of significations can be introduced.

scholarly journals Lambek's operational categories

1986 ◽  
Vol 33 (2) ◽  
pp. 161-175 ◽  
Author(s):  
C. B. Jay
Keyword(s):  
Internal Structure ◽  
Equational Theory ◽  
Categories And Functors

An operational category is a category of models for an equational theory where the interpretation of some operations is predetermined. Examples include the equational and co-equational categories of Linton, categories of functors preserving some class of limits, and algebras for a prop as defined by MacLane. The chief result is a characterisation of the operational categories and functors in terms of their internal structure.

Sign in / Sign up

Export Citation Format

Share Document