Pith. Sign in

RECORD

Corner replacement for Morita contexts

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Raphael Bennett-Tennenhaus

Representation Theory · Submitted 23 Jan 2023

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

The authors' main claim Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence ascends.

how it is stated · asserted 0.97 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2301.09518 (version 2)
Pith IDRPZL5U64, Pith's permanent record of this paper and its review
CitationRaphael Bennett-Tennenhaus. "Corner replacement for Morita contexts." arXiv:2301.09518 (2023). https://pith.science/paper/RPZL5U64
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,564 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider how Morita equivalences are compatible with the notion of a corner subring. Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence ascends. We use the language of Morita contexts, and then specify these more general results. We give applications to trivial extensions of finite-dimensional algebras, tensor rings of pro-species, semilinear clannish algebras arising from orbifolds, and functor categories.

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 consider how Morita equivalences are compatible with the notion of a corner subring. contribution 0.51 0.46 0.10 unclear 0.62
s1 Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence ascends. contribution 0.99 0.93 0.46 asserted 0.97
s2 We use the language of Morita contexts, and then specify these more general results. method 0.96 0.88 0.07 asserted 0.93
s3 We give applications to trivial extensions of finite-dimensional algebras, tensor rings of pro-species, semilinear clannish algebras arising from orbifolds, and functor categories. contribution 0.92 0.89 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.83 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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 consider how Morita equivalences are compatible with the notion of a corner subring. Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence ascends. We use the language of Morita contexts, and then specify these more general results. We give applications to trivial extensions of finite-dimensional algebras, tensor rings of pro-species, semilinear clannish algebras arising from orbifolds, and functor categories.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.