All Questions
Tagged with foundations higher-category-theory
7 questions
24
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2
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2k
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Foundations and contradictions of Scholze's work: the category of presentable infinity categories contains itself
Preface: I am not an expert in the work of Scholze, or anything for that matter.
Question
Has Scholze stated what axioms he is using to develop his theory of motives and analytic geometry. In the ...
- 383
3
votes
1
answer
431
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Does the concept of a $\infty$-category have a natural definition in the $\infty$-world?
I start with a thesis: the natural notion of equality is additional data (paths/morphisms), not a binary relation (the fact that they exist). So, in particular, with such a constructivization (...
- 6,962
4
votes
1
answer
427
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Homotopical realizability
After a long story of dancing around the effective topos $ \mathcal{Eff}$, I finally resolved to get to the bottom of it. To this effect, working as it were backward, I ended up revisiting Kleene's ...
- 7,853
13
votes
3
answers
1k
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Elementary theory of the category of groupoids?
One axiomatisation of set theory, the Elementary Theory of the Category of Sets, or ETCS for short, comes from category theory and states that sets and functions form a locally cartesian-closed, ...
user173426
5
votes
0
answers
219
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Are any formal systems based upon the idea of "iterated characterization pushing" currently in existence? If not, is anyone working on them?
I had an idea in regards to the design of formal systems with foundational aspirations.
To convey the idea, let's talk a bit about the second-order Peano axioms. The way these axioms work, we have a ...
- 3,793
0
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0
answers
410
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Set as a (strict) infinite-category?
First, let me say that I have no idea if such a post has its place here. However, I believe that the ideas I'm going to present are important. The goal of this thread is three fold:
1) trying to ...
- 438
6
votes
1
answer
808
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Untyped Higher Category Theory
I am currently trying to wade through the vast lake of higher category theory, a formidable task,or so it seems.
In the process, it has occurred to me that there is a basic analogy in place with ...
- 7,853