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Questions tagged [category-theory]

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Is category theory as philosophically intuitive as basic logic?

So far as I understand, category theory can be used as foundations of mathematics as in that the rest of logic can be defined through categorical ideas. However is category theory as natural a ...
Babu's user avatar
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3 votes
2 answers
221 views

How might one fundamentally define the difference between indefinite and definite nouns?

I am exploring ologs, a way of diagramming conceptual relationships. I am trying to understand if it is necessary for the nodes or objects of an olog to should be restricted to represent only classes ...
Julius Hamilton's user avatar
1 vote
2 answers
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What does philosophy have to do with category theory? [closed]

Category theory seems very abstract and unrelated to philosophy. Why does it seem to be a part of philosophy? Is category theory used in philosophy and in the development of logical arguments? Isn't ...
ale_7's user avatar
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3 votes
2 answers
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Evil as the opposite category of 𝐕𝐚𝐥𝐮𝐞

Presupposition of the question: the drastic-difference thesis, which is here based on the SEP article on the concept of evil: Since World War II, moral, political, and legal philosophers have become ...
Kristian Berry's user avatar
4 votes
0 answers
98 views

Self-duality (in category theory) and advaita (non-duality in metaphysics)

In category theory, there are self-dual objects, where A ≅ A∗ (A is isomorphic to its dual), with the strict, but possibly non-coherent, case being when A equals A∗ (see Selinger[??]). In some ...
Kristian Berry's user avatar
3 votes
0 answers
70 views

Rather than "ought to be true = is true" being impossible, might it not just be a trivial stage of moral representation?

I just finished reading Eugenia Cheng's essay on moral phraseology in mathematics, and so I want to go over something she says on pg. 20: A recent lecturer of Part III Category Theory declared that ...
Kristian Berry's user avatar
1 vote
0 answers
47 views

Initial/terminal values in a category of values (instead of intrinsic/final vs. extrinsic/instrumental values)

It seems as if the concept of intrinsic value is so unclear and/or unstable that we can't even tell whether (or when) it is transitiveT: First, there is the possibility that the relation of intrinsic ...
Kristian Berry's user avatar
3 votes
2 answers
80 views

Is Kant's talk of "homogeneity" the deeper point-of-contact between his theory of categories, and modern category theory?

The SEP article on category theory says: Categories, functors, natural transformations, limits and colimits appeared almost out of nowhere in a paper by Eilenberg & Mac Lane (1945) entitled “...
Kristian Berry's user avatar
2 votes
1 answer
77 views

Do models of Cartesian closed logic physically exist?

Cartesian closed logics, also known as simple type theories or simply-typed lambda calculi, are ubiquitous; we use sentential logic (WP, nLab) all the time in philosophy and law, and doxastic logic to ...
Corbin's user avatar
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2 votes
0 answers
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A concept of strong free will that's able to be represented in category theory?

Are there any such things as category theories where the category is an indeterminist/postdeterminist form of free will? Let's say, maybe it is a category where each object is an object of choice, ...
Kristian Berry's user avatar
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Is category theory an example of foundherentism?

After reading this essay about the history of type theory, I have refined my assessment of the set- vs. type-theory question in two ways. More similarly to what I was thinking before, I still ground ...
Kristian Berry's user avatar
1 vote
3 answers
87 views

Why do certain ways of categorizing make sense more than others? Is this the intuition behind natural kinds?

From my understanding, natural kinds are kinds that in some way don’t depend on the motivation of the person. In this very specific sense, how can anything adhere to this requirement? Even a single ...
user avatar
4 votes
5 answers
314 views

In category theory, why do we meet more left adjoints than right adjoints

In this answer, the author states that "many of the naturally occurring functors we meet tend to have left adjoint but often they lack right adjoints". Is there any philosophical explanation ...
Bob's user avatar
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Mathematical "forms" as a relation of varying arity

This might be more a MathSE question, but on the other hand, it would involve a peculiar reimagining of the relation between set theory and type theory, so I'll try it out here. OK, so earlier I ...
Kristian Berry's user avatar
11 votes
3 answers
6k views

Set theory vs. type theory vs. category theory

IIRC, in the univalent-foundations program (per Voevodsky), category theory is represented as a possible sort of evolution or new wave of type theory. Maybe my memory is off, but anyway, in nlab they ...
Kristian Berry's user avatar