scholarly journals Enriched category as a model of qualia structure based on similarity judgements

2021 ◽  
Author(s):  
Naotsugu Tsuchiya ◽  
Hayato Saigo ◽  
Steven Phillips
Keyword(s):  
Category Theory ◽  
The Other ◽  
Perceived Similarity ◽  
Enriched Category ◽  
Enriched Categories ◽  
Important Extension ◽  
Similarity Relationships ◽  
Yoneda Lemma ◽  
Similarity Judgements ◽  
Qualia Structure

Qualitative relationships between two instances of conscious experiences can be quantified through the perceived similarity. Previously, we proposed that by defining similarity relationships as arrows and conscious experiences as objects, we can define a category of qualia in the context of category theory. However, the example qualia categories we proposed were highly idealized and limited to cases where perceived similarity is binary: either present or absent without any gradation. Here, we introduce enriched category theory to address the graded levels of similarity that arises in many instances of qualia. Enriched categories generalize the concept of a relation between objects as a directed arrow (or morphism) in ordinary category theory to a more flexible notion, such as a measure of distance. As an alternative relation, here we propose a graded measure of perceived dissimilarity between the two objects. We claim that enriched categories accommodate various types of conscious experiences. An important extension of this claim is the application of the Yoneda lemma in enriched category; we can characterize a quale through a collection of relationships between the quale and the other qualia up to an (enriched) isomorphism.

scholarly journals Enriched category as a model of qualia structure based on similarity judgements

2021 ◽  
Author(s):  
Naotsugu Tsuchiya ◽  
Steven Phillips ◽  
Hayato Saigo
Keyword(s):  
Category Theory ◽  
Sorites Paradox ◽  
Perceived Similarity ◽  
Enriched Category ◽  
Enriched Categories ◽  
Important Extension ◽  
Similarity Relationships ◽  
Yoneda Lemma ◽  
Similarity Judgements ◽  
Qualia Structure

Qualitative relationships between two instances of conscious experiences can be quantified through the perceived similarity. Previously, we proposed that by defining similarity relationships as arrows and conscious experiences as objects, we can define a category of qualia in the context of category theory. However, the example qualia categories we proposed were highly idealized and limited to cases where perceived similarity is binary: either present or absent without any gradation. When similarity is graded, a situation can arise where A0 is similar to A1, A1 is similar to A2, and so on, yet A0 is not similar to An, which is called the Sorites paradox. Here, we introduce enriched category theory to address this situation. Enriched categories generalize the concept of a relation between objects as a directed arrow (or morphism) in ordinary category theory to a more flexible notion, such as a measure of distance. As an alternative relation, here we propose a graded measure of perceived dissimilarity between the two objects. These measures combine in a way that addresses the Sorites paradox; even if the dissimilarity between Ai and Ai+1 is small for i = 0 … n, hence perceived as similar, the dissimilarity between A0 and An can be large, hence perceived as different. In this way, we show how dissimilarity-enriched categories of qualia resolve the Sorites paradox. We claim that enriched categories accommodate various types of conscious experiences. An important extension of this claim is the application of the Yoneda lemma in enriched category; we can characterize a quale through a collection of relationships between the quale and the other qualia up to an (enriched) isomorphism.

scholarly journals THH and Traces of Enriched Categories

2020 ◽  
Author(s):  
John D Berman
Keyword(s):  
Category Theory ◽  
Hochschild Homology ◽  
Independent Interest ◽  
Elementary Model ◽  
Enriched Category ◽  
Enriched Categories ◽  
Higher Category Theory ◽  
Model Independent ◽  
Universal Construction ◽  
Topological Hochschild Homology

Abstract We prove that topological Hochschild homology (THH) arises from a presheaf of circles on a certain combinatorial category, which gives a universal construction of THH for any enriched $\infty $-category. Our results rely crucially on an elementary, model-independent framework for enriched higher-category theory, which may be of independent interest. For those interested only in enriched category theory, read Sections 1.3 and 2.

Completions of Non-Symmetric Metric Spaces Via Enriched Categories

2009 ◽  
Vol 16 (1) ◽  
pp. 157-182
Author(s):  
Vincent Schmitt
Keyword(s):  
Category Theory ◽  
Metric Spaces ◽  
Enriched Category ◽  
Closed Category ◽  
Enriched Categories ◽  
Terminal Object ◽  
Base Category ◽  
Monoidal Closed Category ◽  
The One ◽  
Universal Completion

Abstract It is known from [Lawvere, Repr. Theory Appl. Categ. 1: 1–37 2002] that nonsymmetric metric spaces correspond to enrichments over the monoidal closed category [0, ∞]. We use enriched category theory and in particular a generic notion of flatness to describe various completions for these spaces. We characterise the weights of colimits commuting in the base category [0, ∞] with the conical terminal object and cotensors. Those can be interpreted in metric terms as very general filters, which we call filters of type 1. This correspondence extends the one between minimal Cauchy filters and weights which are adjoint as modules. Translating elements of enriched category theory into the metric context, one obtains a notion of convergence for filters of type 1 with a related completeness notion for spaces, for which there exists a universal completion. Another smaller class of flat presheaves is also considered both in the context of both metric spaces and preorders. (The latter being enrichments over the monoidal closed category 2.) The corresponding completion for preorders is the so-called dcpo completion.

scholarly journals A relational approach to consciousness: categories of level and contents of consciousness

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Naotsugu Tsuchiya ◽  
Hayato Saigo
Keyword(s):  
Empirical Research ◽  
Category Theory ◽  
Gold Standard ◽  
Empirical Testing ◽  
Relational Approach ◽  
Alternative Approach ◽  
Key Concepts ◽  
Categorical Structure ◽  
Yoneda Lemma ◽  
Qualia Structure

Abstract Characterizing consciousness in and of itself is notoriously difficult. Here, we propose an alternative approach to characterize, and eventually define, consciousness through exhaustive descriptions of consciousness’ relationships to all other consciousness. This approach is founded in category theory. Indeed, category theory can prove that two objects A and B in a category can be equivalent if and only if all the relationships that A holds with others in the category are the same as those of B; this proof is called the Yoneda lemma. To introduce the Yoneda lemma, we gradually introduce key concepts of category theory to consciousness researchers. Along the way, we propose several possible definitions of categories of consciousness, both in terms of level and contents, through the usage of simple examples. We propose to use the categorical structure of consciousness as a gold standard to formalize empirical research (e.g. color qualia structure at fovea and periphery) and, especially, the empirical testing of theories of consciousness.

scholarly journals Cartesian Differential Categories as Skew Enriched Categories

2021 ◽  
Author(s):  
Richard Garner ◽  
Jean-Simon Pacaud Lemay
Keyword(s):  
Linear Logic ◽  
Usual Sense ◽  
Enriched Category ◽  
Enriched Categories ◽  
Full Structure ◽  
Monoidal Closed Category ◽  
Category Of Modules ◽  
Differential Categories ◽  
Linear Category ◽  
Open Question

AbstractWe exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rig k. However, the tensor product on this category is not the usual one, but rather a warping of it by a certain monoidal comonad Q. Thus the enrichment base is not a monoidal category in the usual sense, but rather a skew monoidal category in the sense of Szlachányi. Our first main result is that cartesian differential categories are the same as categories with finite products enriched over this skew monoidal base. The comonad Q involved is, in fact, an example of a differential modality. Differential modalities are a kind of comonad on a symmetric monoidal k-linear category with the characteristic feature that their co-Kleisli categories are cartesian differential categories. Using our first main result, we are able to prove our second one: that every small cartesian differential category admits a full, structure-preserving embedding into the cartesian differential category induced by a differential modality (in fact, a monoidal differential modality on a monoidal closed category—thus, a model of intuitionistic differential linear logic). This resolves an important open question in this area.

Excès du témoignage, déhiscence du témoin. Søren Kierkegaard, Emmanuel Lévinas, Jean-Louis Chrétien

2021 ◽  
Vol 21 ◽  
pp. 129-151
Author(s):  
Rodolphe Olcèse ◽  
Keyword(s):  
Emmanuel Levinas ◽  
Soren Kierkegaard ◽  
The Other ◽  
Subjective Truth ◽  
Important Extension ◽  
The Voice

This text articulates the concept of subjective truth developed by Søren Kierkegaard in Concluding Unscientific Postscript to Philosophical Fragments, in connection to a conception of testimony which both exceeds and reveals the possibilities of thinking and acting of the witness. This imbalance between the testimony and the witness finds an important extension in the distinction between the Saying and the Said made by Emmanuel Lévinas in Otherwise than Being, or Beyond Essence. This distinction opens up an understanding of thought as affectivity and allows witnessing to be viewed in the light of responsibility to the other. By being part of this philosophical heritage, Jean-Louis Chrétien shows how the testimony of the infinite is also phenomenalized in the experience of a chant that discovers its own modalities in this excess of beauty on the voice that tries to say it.

scholarly journals THE SOCIAL NETWORK OF CONTEMPORARY POPULAR MUSICIANS

2007 ◽  
Vol 17 (07) ◽  
pp. 2281-2288 ◽  
Author(s):  
JUYONG PARK ◽  
OSCAR CELMA ◽  
MARKUS KOPPENBERGER ◽  
PEDRO CANO ◽  
JAVIER M. BULDÚ
Keyword(s):  
Social Networks ◽  
Social Network ◽  
The Other ◽  
Collaboration Network ◽  
Perceived Similarity ◽  
Similarity Network ◽  
Self Organized ◽  
The Social ◽  
Information Database

In this paper, we analyze two social network datasets of contemporary musicians constructed from allmusic.com (AMG), a music and artists' information database: one is the collaboration network in which two musicians are connected if they have performed or produced an album together, and the other is the similarity network in which they are connected if they were musically similar according to the music experts. We find that, while both networks exhibit typical features of social networks such as high transitivity (clustering), we find that they differ significantly in some key network features such as the degree and the betweenness distributions. We believe that this highlights the fundamental differences in the construction mechanism (self-organized collaboration and human-perceived similarity) of the new networks.

Replacement between Conformity and Counter-Conformity in Consumption Decisions

2013 ◽  
Vol 112 (1) ◽  
pp. 125-150 ◽  
Author(s):  
Ting-Jui Chou ◽  
Qi Dai ◽  
En-Chung Chang ◽  
Veronica Wong
Keyword(s):  
Theoretical Model ◽  
Cognitive Dissonance ◽  
Self Esteem ◽  
The Other ◽  
Perceived Similarity ◽  
Chinese Context ◽  
Self Perceptions ◽  
Consumption Decisions ◽  
Conformity Behavior ◽  
The Way

This study assessed, in a Chinese context, how self-esteem interacts with perceived similarity and uniqueness to yield cognitive dissonance, and whether the dissonance leads to self-reported conformity or counter-conformity behavior. Participants were 408 respondents from 4 major Chinese cities ( M age = 33.0 yr., SD = 4.3; 48% men). Self-perceptions of uniqueness, similarity, cognitive dissonance, self-esteem and need to behave in conformity or counter-conformity were measured. A theoretical model was assessed in four situations, relating the ratings of self-esteem and perceived similarity/uniqueness to the way other people at a wedding were dressed, and the resultant cognitive dissonance and conformity/counter-conformity behavior. Regardless of high or low self-esteem, all participants reported cognitive dissonance when they were told that they were dressed extremely similarly to or extremely differently from the other people attending the wedding. However, the conforming/counter-conforming strategies used by participants to resolve the cognitive dissonance differed. When encountering dissonance induced by the perceived extreme uniqueness of dress, participants with low self-esteem tended to say they would dress next time so as to conform with the way others were dressed, while those with high self-esteem indicated they would continue their counter-conformity in attire. When encountering dissonance induced by the perceived extreme similarity to others, both those with high and low self-esteem tended to say they would dress in an unorthodox manner to surprise other people in the future.

Yoneda lemma for enriched ∞-categories

2020 ◽  
Vol 367 ◽  
pp. 107129
Author(s):  
Vladimir Hinich
Keyword(s):  
Enriched Categories ◽  
Yoneda Lemma
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