All Questions
Tagged with philosophy category-theory
30
questions
2
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1
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133
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Definite description in homotopy type theory
I asked this question there and I have been suggested to ask it here.
In a paper by David Corfield, we have an account of definite description in homotopy type theory. The author gives the following ...
- 308
0
votes
2
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75
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For every object, is there a unique notion of isomorphism?
Do you think that, according to most mathematicians, the following claim holds?
(Claim) For every object, there is a unique notion of isomorphism.
Perhaps one might think that for some sets, such as $(...
- 57
2
votes
1
answer
95
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Is there a precise definition to "interpretation" in Mathematics?
A category (as distinguished from a metacategory) will mean any interpretation of the category axioms within set theory. Here are the details.
Sect-2,page-10, Category Theory for the Working ...
1
vote
1
answer
207
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Is the term "category" in Category theory entirely different from the category in topological spaces?
$(X, \tau) $ be a topological space.
$A\subset X$ is said to be first category (meager) if it can be expressed as a countable union of nowhere dense sets. Otherwise we call the set $A$ second ...
- 13k
2
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0
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75
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Why do we care about non-equal but isomorphic objects in a category?
Note: this is more of a philosophical question.
Said differently, what if we were to ask Categories to be extensional in the sense that if two objects are isomorphic then they are equal?
Is there any ...
- 1,347
4
votes
1
answer
141
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Is there a category (or rather a mathematical theory) for which we know a lot about, but not whether its object class is empty or not?
this is a bit of a vague question so let me describe a bit what motivates it: Yesterday I was reading the Wikipedia article about perfect numbers, where I find the section https://en.wikipedia.org/...
- 117
3
votes
2
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300
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Morphism composition is the property of morphism or the structure of category?
In the definition of category, there is a morphism composition law. If A, B, C are objects, and if f is a morphism from A to B, g is a morphism from B to C, then there is a corresponding morphism from ...
- 371
4
votes
1
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252
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Reference request for subjective/objective logic for mathematicians
I am self-learning William Lawvere's Conceptual Mathematics and Sets For Mathematics. He mentioned subjective and objective logic. I really don't understand it. Do I have to read Hegel's to fully ...
- 602
0
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1
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150
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Why do we *restrict* to universes instead of *surrounding* us with them?
In set theory and category theory one easily runs into the problem of size. For example Russell's paradox tells us that it is impossible to have consistent set theory allowing a set of all sets. ...
- 11.2k
4
votes
0
answers
87
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Non-associativeness of composition in deductive systems?
WARNING: The first three and last two paragraphs of this question concern historical/philosophical matters related to a secondary aim of the question. If you are more interested in the properly ...
- 697
0
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0
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86
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Why I should not study embedded categories?
In my lecture course of representation theory of $K$-algebras, we embedded the category of $A$-modules (where $A$ is an associative unital $K$-algebra) into the category of $K<X_i|i\in I>$-...
user657166
14
votes
1
answer
2k
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Examples of co-implication (a.k.a co-exponential)
In Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research Yaroslav Shramko, inspired by Popper, makes an interesting case that co-constructive logic as the logic of ...
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17
votes
6
answers
3k
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What exactly is an arrow in a category?
The usual definition of a category states: a category $\mathbf{C}$ consists of:
A collection $\text{ob}(\mathbf{C})$ of objects
A collection $\text{arr}(\mathbf{C})$ of arrows
Some rules on the ...
- 3,226
1
vote
1
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179
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How Topos "connect" continuous and discrete
I'm not a mathematician, but I have some knowledge in Category theory (mainly from computer science background).
As I understand it, Topoi, and in particular presheaf category can "capture" the ...
- 159
2
votes
1
answer
118
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Choice of closed monoidal structure
This might be a somewhat philosophical question in category theory. I sometimes have trouble understanding with some monoidal structures defined, why the one we choose are the "good ones". For example,...
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