scholarly journals An Essential, Hyperconnected, Local Geometric Morphism that is not Locally Connected

Author(s):  
Jens Hemelaer ◽  
Morgan Rogers

AbstractThomas Streicher asked on the category theory mailing list whether every essential, hyperconnected, local geometric morphism is automatically locally connected. We show that this is not the case, by providing a counterexample.

Moreana ◽  
1969 ◽  
Vol 6 (Number 23) (3) ◽  
pp. 8-23
Keyword(s):  

Moreana ◽  
1966 ◽  
Vol 3 (Number 11) (3) ◽  
pp. 5-20
Keyword(s):  

ADALAH ◽  
2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Munadhil Abdul Muqsith

Abstract:The internet developed for the first time in Indonesia in the early 1990s. Starting from the pagayuban network, it is now expanding without boundaries anywhere. A survey conducted by the Indonesian Internet Service Providers Association (APJII) said that the number of internet users in Indonesia in 2012 reached 63 million people or 24.23 percent of the country's total population. Next year, that figure is predicted to increase by close to 30 percent to 82 million users and continue to grow to 107 million in 2014 and 139 million or 50 percent of the total population in 2015. million people. This matter also results in political communication with the internet media, or is often said to be cyber politics. Cyber politics in Indonesia has faced growth in recent years. There are many facilities that support the growth of cyber politics, such as Facebook, Twitter, mailing list, YouTube, and others.Keywords: Cyberpolitik, Internet  Abstrak:Internet berkembang pertama kali di Indonesia pada awal tahun 1990-an. Diawali dari pagayuban network kini berkembang luas tanpa batas dimanapun juga. Suatu survei yang diselenggarakan Asosiasi Penyelenggara Jasa Internet Indonesia (APJII) mengatakan kalau jumlah pengguna internet di Indonesia tahun 2012 menggapai 63 juta orang ataupun 24,23 persen dari total populasi negeri ini. Tahun depan, angka itu diprediksi naik dekat 30 persen jadi 82 juta pengguna serta terus berkembang jadi 107 juta pada 2014 serta 139 juta ataupun 50 persen total populasi pada 2015. juta orang. Perihal ini pula berakibat pada komunikasi politik dengan media internet, ataupun kerap diucap dengan cyber politic. Cyber politic di Indonesia hadapi pertumbuhan sebagian tahun terakhir. Banyaknya fasilitas yang menunjang pertumbuhan cyber politic semacam terdapatnya facebook, Twitter, mailing list, youtobe, serta lain-lain.Kata Kunci: Cyberpolitik, Internet 


2020 ◽  
Author(s):  
Shunsuke Ikeda ◽  
Miho Fuyama ◽  
Hayato Saigo ◽  
Tatsuji Takahashi

Machine learning techniques have realized some principal cognitive functionalities such as nonlinear generalization and causal model construction, as far as huge amount of data are available. A next frontier for cognitive modelling would be the ability of humans to transfer past knowledge to novel, ongoing experience, making analogies from the known to the unknown. Novel metaphor comprehension may be considered as an example of such transfer learning and analogical reasoning that can be empirically tested in a relatively straightforward way. Based on some concepts inherent in category theory, we implement a model of metaphor comprehension called the theory of indeterminate natural transformation (TINT), and test its descriptive validity of humans' metaphor comprehension. We simulate metaphor comprehension with two models: one being structure-ignoring, and the other being structure-respecting. The former is a sub-TINT model, while the latter is the minimal-TINT model. As the required input to the TINT models, we gathered the association data from human participants to construct the ``latent category'' for TINT, which is a complete weighted directed graph. To test the validity of metaphor comprehension by the TINT models, we conducted an experiment that examines how humans comprehend a metaphor. While the sub-TINT does not show any significant correlation, the minimal-TINT shows significant correlations with the human data. It suggests that we can capture metaphor comprehension processes in a quite bottom-up manner realized by TINT.


Author(s):  
Michael Ernst

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.


Author(s):  
Ash Asudeh ◽  
Gianluca Giorgolo

This book presents a theory of enriched meanings for natural language interpretation. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings just when required compositionally, which avoids generalizing meanings to the worst case. The theory is captured formally using monads, a concept from category theory. Monads are also prominent in functional programming and have been successfully used in the semantics of programming languages to characterize certain classes of computation. They are used here to model certain challenging linguistic computations at the semantics/pragmatics boundary. Part I presents some background on the semantics/pragmatics boundary, informally presents the theory of enriched meanings, reviews the linguistic phenomena of interest, and provides the necessary background on category theory and monads. Part II provides novel compositional analyses of the following phenomena: conventional implicature, substitution puzzles, and conjunction fallacies. Part III explores the prospects of combining monads, with particular reference to these three cases. The authors show that the compositional properties of monads model linguistic intuitions about these cases particularly well. The book is an interdisciplinary contribution to Cognitive Science: These phenomena cross not just the boundary between semantics and pragmatics, but also disciplinary boundaries between Linguistics, Philosophy and Psychology, three of the major branches of Cognitive Science, and are here analyzed with techniques that are prominent in Computer Science, a fourth major branch. A number of exercises are provided to aid understanding, as well as a set of computational tools (available at the book's website), which also allow readers to develop their own analyses of enriched meanings.


Author(s):  
Jumoke Abass Alesinloye ◽  
Eoin Groarke ◽  
Jaganath Babu ◽  
Subathra Srinivasan ◽  
Greg Curran ◽  
...  

1997 ◽  
Vol 29 (2) ◽  
pp. 40-43
Author(s):  
Gary Perlman
Keyword(s):  

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.


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