Question

Asked 20th Feb, 2022

Universidade Aberta

How can I find a list of open problems in Homotopy Type Theory and Univalent Foundations ?

Type Theory

Foundations

Logic

Logic and Foundations of Mathematics

Artificial Intelligence

César De Jesus Rodrigues

University of Minho

A list of open problrems for hpmotopy type theory is presented in HISTORIC.

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Cyprien Saito

Ecole Normale Supérieure de Paris

Probably there does not exist such a list. My advice is for you is that you can find out by yourself such a type of problems today. The point is the localization of base change conditions in the formality of discrete topology. My suggestion concerns naturally my original researches. That is, measure theories on mixed motives. Or cercle method on mixed motives as the prolongement-localization of zeta function. See my such kind of articles and please examine the concreteness of its nouveauté.

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Adnan Majeed

USA Foundation Lahore

read this article

https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/preface-to-the-mscs-issue-311-2021-homotopy-type-theory-and-univalent-foundations-part-ii/FC0169CAA8492AEB519AD96090870B08

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Germán Benitez Monsalve

Federal University of Amazonas

Dear,

Clarence Lewis Protin

I recommend you the following website

http://128.2.67.219/homotopytypetheory/show/open+problems

Regards.

Germán Benitez

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César De Jesus Rodrigues

University of Minho

A list of open problrems for hpmotopy type theory is presented in HISTORIC.

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Is this a new scam or something reliable?

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862 answers

Asked 4th Aug, 2020

Jean-Claude Grivel

Dear colleagues,

Today I received an email from "awards@scienceconnect.online" with the following text:

Dear Author,

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There was also a nomination link, which I removed from the text above and that I did not try to open, as well as the abstract of a paper that was accepted a few days ago and made available online about 10 hours before that mail was being sent. According to the website (https://sciencefather.com/awards/), one needs to pay a registration fee in order to apply for an award. Is this a new scam? Thanks for your help.

How to add a link to my publication?

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Asked 28th Feb, 2020

Maritta Törrönen

The book I have edited with my colleagues is now published open access. This is the link to the publication https://helda.helsinki.fi/handle/10138/311959. How to add this to the publication because it is not a file, it is a link?

Thank you!

Maritta Törrönen

The significance of category theory for philosophy

Discussion

219 replies

Asked 29th Apr, 2019

Thomas Krantz

1) There is some tradition in philosophy of mathematics starting at the late 19th century and culminating in the crisis of foundations at the beginning of the 20th century. Names here are Zermelo, Frege, Whitehead and Russel, Cantor, Brouwer, Hilbert, Gödel, Cavaillès, and some more. At that time mathematics was already focused on itself, separated from general rationalist philosophy and epistemology, from a philosophy of the cosmos and the spirit.

2) Stepping backwards in time we have the great “rationalist” philosophers of the 17th, 18th, 19th century: Descartes, Leibniz, Malebranche, Spinoza, Hegel proposing a global view of the universe in which the subject, trying to understand his situation, is immersed.

3) Still making a big step backwards in time, we have the philosophers of the late antiquity and the beginning of our era (Greek philosophy, Neoplatonist schools, oriental philosophies). These should not be left out from our considerations.

4) Returning to the late 20th century we see inside mathematics appears the foundation (Eilenberg, Lavwere, Grothendieck, Maclane,…) of Category theory, which is in some sense a transversal theory inside mathematics. Among its basic principles are the notions of object, arrow, functor, on which then are founded adjunctions, (co-)limits, monads, and more evolved concepts.

Do you think these principles have their signification a) for science b) the rationalist philosophies we described before, and ultimately c) for more general philosophies of the cosmos?

Examples: The existence of an adjunction of two functors could have a meaning in physics e.g.. The existence of a natural numbers - object known from topos theory could have philosophical consequences. (cf. Immanuel Kant, Antinomien der reinen Vernunft).

If every neuron in a human was accurately simulated in a computer, would it result in human consciousness?

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Kirk MacGregor

Why or why not?

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Jonathan Robert Brewster Fisher

I'm asking because I just had an article come out in a journal that embargoes uploading an accepted manuscript on researchgate but allows me to post it to my personal web site.

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