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Injective objects and retracts of Fra\"iss\'e limits

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Wieslaw Kubiś

Category Theory · Submitted 22 Jul 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It turns out that retracts of Fra\"iss\'e limits are precisely the objects that are injective relatively to such a pair.

how it is stated · asserted 1.00 read the record →

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arXiv ID1107.4620 (version 4)
Pith IDBTCSNGPU, Pith's permanent record of this paper and its review
CitationWieslaw Kubi\'s. "Injective objects and retracts of Fra\"iss\'e limits." arXiv:1107.4620 (2011). https://pith.science/paper/BTCSNGPU
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,536 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). It turns out that retracts of Fra\"iss\'e limits are precisely the objects that are injective relatively to such a pair. One of the applications is a characterization of non-expansive retracts of Urysohn's universal metric space.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. contribution 0.95 0.94 0.49 asserted 1.00
s1 For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). method 0.92 0.82 0.03 asserted 0.88
s2 It turns out that retracts of Fra\"iss\'e limits are precisely the objects that are injective relatively to such a pair. result 1.00 0.91 0.89 asserted 1.00
s3 One of the applications is a characterization of non-expansive retracts of Urysohn's universal metric space. result 0.74 0.84 0.06 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). It turns out that retracts of Fra\"iss\'e limits are precisely the objects that are injective relatively to such a pair. One of the applications is a characterization of non-expansive retracts of Urysohn's universal metric space.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 7 sentences without a confident label

Compares with 1 paper
Cites as background 1 paper

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