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An inverse Fra\"iss\'e limit for finite posets and duality for posets and lattices

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Szymon G{l}a̧b, Micha{l} Pawlikowski

Combinatorics · Submitted 25 Jan 2022

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

The authors' main claim Each of these two sequences has a limit object -- an inverse limit, which is an object of our interest as well.

how it is stated · asserted 1.00 read the record →

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arXiv ID2201.10302 (version 1)
Pith IDEFPHXHKZ, Pith's permanent record of this paper and its review
CitationMicha{\l} Pawlikowski, Szymon G{\l}\c{a}b. "An inverse Fra\"iss\'e limit for finite posets and duality for posets and lattices." arXiv:2201.10302 (2022). https://pith.science/paper/EFPHXHKZ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,947 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of lattices associated with it. Each of these two sequences has a limit object -- an inverse limit, which is an object of our interest as well. In the first chapter there are some preliminaries considering partial orders, lattices, topology, inverse limits, category theory and Fra\"iss\'e theory, which are used later. In the second chapter there are our results considering a Fra\"iss\'e sequence in category of finite posets with quotient maps and properties of inverse limit of this sequence. In the third chapter we investigate connections between posets and order ideals corresponding to them, getting an inductive sequence made of these ideals; then we study properties of the inverse limit of this sequence.

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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 consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. contribution 0.77 0.95 0.08 asserted 1.00
s1 Then we use commonly known relations between partial orders and lattices to construct a sequence of lattices associated with it. method 0.88 0.90 0.06 asserted 1.00
s2 Each of these two sequences has a limit object -- an inverse limit, which is an object of our interest as well. result 0.48 0.71 0.13 asserted 1.00
s3 In the first chapter there are some preliminaries considering partial orders, lattices, topology, inverse limits, category theory and Fra\"iss\'e theory, which are used later. background 0.96 0.21 0.02 asserted 0.99
s4 In the second chapter there are our results considering a Fra\"iss\'e sequence in category of finite posets with quotient maps and properties of inverse limit of this sequence. contribution 0.95 0.94 0.19 asserted 0.95
s5 In the third chapter we investigate connections between posets and order ideals corresponding to them, getting an inductive sequence made of these ideals; then we study properties of the inverse limit of this sequence. contribution 0.94 0.94 0.14 asserted 0.99

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

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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 consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of lattices associated with it. Each of these two sequences has a limit object -- an inverse limit, which is an object of our interest as well. In the first chapter there are some preliminaries considering partial orders, lattices, topology, inverse limits, category theory and Fra\"iss\'e theory, which are used later. In the second chapter there are our results considering a Fra\"iss\'e sequence in category of finite posets with quotient maps and properties of inverse limit of this sequence. In the third chapter we investigate connections between posets and order ideals corresponding to them, getting an inductive sequence made of these ideals; then we study properties of the inverse limit of this sequence.

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