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10prompts.txt
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10prompts.txt
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%% Building an NLI corpus from TAC sentences/Revised prompts after chatGPT/GPT4 checks and discussion
1. We use a number of interesting categories related to probability theory.
E. There exists a number of interesting categories related to probability theory.
1. We use a number of interesting categories related to probability theory.
C. There are no interesting categories related to probability theory.
1. We use a number of interesting categories related to probability theory.
N. There are no interesting categories related to topology.
2. A notion of central importance in categorical topology is that of topological functor.
E. Topological functor is a notion of categorical topology.
2. A notion of central importance in categorical topology is that of topological functor.
C. There are no notions of importance in categorical topology.
2. A notion of central importance in categorical topology is that of topological functor.
N. There are many notions of central importance in categorical topology.
3. In the nilpotent case, this nerve is known to be a Kan complex.
E. There are nerves that are Kan complexes.
3. In the nilpotent case, this nerve is known to be a Kan complex.
C. In the nilpotent case, this nerve is not known to be a Kan complex.
3. In the nilpotent case, this nerve is known to be a Kan complex.
N. This nerve is not known to be a Kan complex.
4. We worked through numerous examples to demonstrate the power of these notions.
E. We worked through two examples to demonstrate the power of these notions.
4. We worked through numerous examples to demonstrate the power of these notions.
C. We did not work through numerous examples to demonstrate the power of these notions.
4. We worked through numerous examples to demonstrate the power of these notions.
N. We worked through more than 20 examples to demonstrate the power of these notions.
5. If the category is additive, we define a sheaf of categories of analytic functions.
E. If the category is additive, we define a sheaf of categories of functions.
5. If the category is additive, we define a sheaf of categories of analytic functions.
C. If the category is additive, we do not define a sheaf of categories of analytic functions.
5. If the category is additive, we define a sheaf of categories of analytic functions.
N: If the category is non-additive, we define a sheaf of categories of analytic functions.
6. We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties.
E. We can define analytic versions of Arakelov compactifications of affine arithmetic varieties.
6. We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties.
C. These relations cannot be used to define analytic versions of Arakelov compactifications of affine arithmetic varieties.
6. We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties.
N: We use these relations to define analytic versions of compactifications of non-varieties.
7. These functors are used in the paper only to prove Corollary~8.3.
E. These functors are used in the paper to prove Corollary~8.3.
7. These functors are used in the paper only to prove Corollary~8.3.
C. These functors are not used in the paper to prove Corollary~8.3.
7. These functors are used in the paper only to prove Corollary~8.3.
N. These natural transformations are used in the paper to prove Corollary~8.5.
8. A proof of this corollary is given without details.
E. There exists a proof of this corollary.
8. A proof of this corollary is given without details.
C. There is no proof of this corollary without details.
8. A proof of this corollary is given without details.
N. A proof of this corollary is given without a computer program.
9. Here ``balanced'' can be omitted if the category is additive.
E. For additive categories ``balanced" can be omitted here.
9. Here ``balanced'' can be omitted if the category is additive.
C. Here ``balanced'' cannot be omitted if the category is additive.
9. Here ``balanced'' can be omitted if the category is additive.
N. Here ``balanced'' can be omitted if the category is multiplicative.
10. We introduce the notion of mutation pairs in pseudo-triangulated categories.
E. We introduce the notion of mutation pairs.
10. We introduce the notion of mutation pairs in pseudo-triangulated categories.
C. We cannot introduce the notion of mutation pairs in pseudo-triangulated categories.
10. We introduce the notion of mutation pairs in pseudo-triangulated categories.
N: We introduce the notation of mutation pairs in monoidal categories.
11. This result unifies many previous constructions of quotient triangulated categories.
E: This result unifies some previous constructions of quotient triangulated categories.
11. This result unifies many previous constructions of quotient triangulated categories.
C: This result is not related to any of the previous constructions of quotient triangulated categories.
11. This result unifies many previous constructions of quotient triangulated categories.
N: This result unifies all previous constructions of quotient triangulated categories.
12. We study extra assumptions on pretopologies that are needed for this theory.
E: We investigate additional assumptions on pretopologies that are needed for this theory.
12. We study extra assumptions on pretopologies that are needed for this theory.
C: However, we will not be concerned with extra assumptions on pretopologies needed for this theory.
12. We study extra assumptions on pretopologies that are needed for this theory.
N: We do not study the basic assumptions on pretopologies that are needed for this theory.
13. We check these extra assumptions in several categories with pretopologies.
E: We check these extra assumptions in at least one category with a pretopology.
13. We check these extra assumptions in several categories with pretopologies.
C: We will not check these extra assumptions in categories with pretopologies.
13. We check these extra assumptions in several categories with pretopologies.
N: We check these extra assumptions in categories with tensor products.
14. Functors between groupoids may be localised at equivalences in two ways.
E: Functors between groupoids can be localised at equivalences.
14. Functors between groupoids may be localised at equivalences in two ways.
C: Unfortunately, it is not possible to localise functors between groupoids at equivalences.
14. Functors between groupoids may be localised at equivalences in two ways.
N: Localisation of functors between groupoids is used to prove Theorem 5.3.
15. We show that both approaches give equivalent bicategories.
E: Both approaches yield equivalent bicategories.
15. We show that both approaches give equivalent bicategories.
C: It was shown that these two approaches give bicategories with very different bicategorical properties.
15. We show that both approaches give equivalent bicategories.
N: Both approaches give the same bicategory.
16. In this paper, we use the language of operads to study open dynamical systems.
E: We study dynamical systems in this paper.
16. In this paper, we use the language of operads to study open dynamical systems.
C: We will not be concerned with the language of operads.
16. In this paper, we use the language of operads to study open dynamical systems.
N: The study of open dynamical systems requires the language of operads.
17. The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams.
E: Wiring diagrams are related to the syntactic architecture of such interconnections.
17. The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams.
C: Such interconnections lack any syntactic structure.
17. The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams.
N: The only way to encode the syntactic structure of such interconnections is by means of the visual language of wiring diagrams.
18. Moreover it enables us to characterise operads as categorical polynomial monads in a canonical way.
E: Operads can be characterised as categorical polynomial monads.
18. Moreover it enables us to characterise operads as categorical polynomial monads in a canonical way.
C: Operads can be characterised as categorical polynomial monads; however, no canonical way of doing so exists.
18. Moreover it enables us to characterise operads as categorical polynomial monads in a canonical way.
N: There is exactly one way to characterise operads as categorical polynomial monads.
19. We have two useful gradings related by isomorphisms which change the degree.
E: There exist some gradings related by isomorphisms which change the degree.
19. We have two useful gradings related by isomorphisms which change the degree.
C: No two gradings which change the degree are isomorphic.
19. We have two useful gradings related by isomorphisms which change the degree.
N: There exist many pairs of gradings related by isomorphisms which change the degree.
20. The result is a double category C//G which describes the local symmetries of C.
E: The result is a category.
20. The result is a double category C//G which describes the local symmetries of C.
C: The result is a double category C//G which does not describe the local symmetries of C.
20. The result is a double category C//G which describes the local symmetries of C.
N: The result describes both local and non-local symmetries of C.
21. There are few known computable examples of non-abelian surface holonomy.
E: There are some known examples of non-abelian surface holonomy.
21. There are few known computable examples of non-abelian surface holonomy.
C: There are no known computable examples of non-abelian surface holonomy.
21. There are few known computable examples of non-abelian surface holonomy.
N: There are few known examples of non-abelian surface holonomy.
22. Using these ideas, we also prove that magnetic monopoles form an abelian group.
E: Using these ideas, we also prove that magnetic monopoles form a group.
22. Using these ideas, we also prove that magnetic monopoles form an abelian group.
C: Using these ideas, we disprove the conjecture that magnetic monopoles form a group.
22. Using these ideas, we also prove that magnetic monopoles form an abelian group.
N: Using these ideas, we also prove that monopoles form an abelian group.
23. We introduce a 3-dimensional categorical structure which we call intercategory.
E: We introduce a 3-dimensional categorical structure.
23. We introduce a 3-dimensional categorical structure which we call intercategory.
C: We introduce a 2-dimensional categorical structure which we call intercategory.
23. We introduce a 3-dimensional categorical structure which we call intercategory.
N: An intercategory is a category with a 3-dimensional intercategorical structure.
24. We show that these fit together to produce a strict triple category of intercategories.
E: We show that these fit together to produce a category of intercategories.
24. We show that these fit together to produce a strict triple category of intercategories.
C: We doubt that these fit together to produce a strict triple category of intercategories.
24. We show that these fit together to produce a strict triple category of intercategories.
N: Three intercategories fit together to produce a strict triple.
25. This is the third paper in a series.
E: This paper is part of a series.
25. This is the third paper in a series.
C: This is the fourth paper in a series.
25. This is the third paper in a series.
N: This is the third paper on this topic.
26. The effect of any bundle of Lie groups is trivial.
E: Lie groups sometimes appear in bundles.
26. The effect of any bundle of Lie groups is trivial.
C: The effect of a bundle of Lie groups is non-trivial.
26. The effect of any bundle of Lie groups is trivial.
N: Groups always have effects.
27. All quotients of a given Lie groupoid determine the same effect.
E: All quotients of a given Lie groupoid determine some effect.
27. All quotients of a given Lie groupoid determine the same effect.
C: Quotients of a Lie groupoid determine different effects.
27. All quotients of a given Lie groupoid determine the same effect.
N: A Lie groupoid has either zero or one quotient.
28. Our analysis is relevant to the presentation theory of proper smooth stacks.
E: Proper smooth stacks may sometimes be presented.
28. Our analysis is relevant to the presentation theory of proper smooth stacks.
C: Our analysis does not have anything to say about the presentation theory of proper smooth stacks.
28. Our analysis is relevant to the presentation theory of proper smooth stacks.
N: Proper smooth stacks may always be presented.
29. This paper extends the Day Reflection Theorem to monoidal categories.
E: This paper extends the Day Reflection Theorem to a family of categories.
29. This paper extends the Day Reflection Theorem to skew monoidal categories.
C: This paper derives the Day Reflection Theorem from skew monoidal categories.
29. This paper extends the Day Reflection Theorem to skew monoidal categories.
N: This paper extends the Day Reflection Theorem to monoidal categories.
30. We also give a presentation for FinRelk.
E: We also exhibit a presentation for FinRelk.
30. We also give a presentation for FinRelk.
C: There is no presentation for FinRelk.
30. We also give a presentation for FinRelk.
N: This is the first time that anyone gives a presentation for FinRelk.