Eilenberg-Kelly Reloaded

Reference. Eilenberg-Kelly Reloaded

Tarmo Uustalu, Niccolò Veltri, Noam Zeilberger · MFPS · 2020 · category-theory · DOI

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Cite as @uustalu-2020-eilenberg (helia, typst) · \cite{uustalu-2020-eilenberg} (LaTeX)

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bibtex · 1 line

@article{uustalu-2020-eilenberg, title={Eilenberg-Kelly Reloaded}, volume={352}, ISSN={1571-0661}, url={http://dx.doi.org/10.1016/j.entcs.2020.09.012}, DOI={10.1016/j.entcs.2020.09.012}, journal={Electronic Notes in Theoretical Computer Science}, publisher={Elsevier BV}, author={Uustalu, Tarmo and Veltri, Niccolò and Zeilberger, Noam}, year={2020}, month=Oct, pages={233–256} }

hayagriva YAML (typst)

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uustalu-2020-eilenberg:
  type: article
  title: Eilenberg-Kelly Reloaded
  author:
  - Uustalu, Tarmo
  - Veltri, Niccolò
  - Zeilberger, Noam
  date: 2020-10
  page-range: 233-256
  url: http://dx.doi.org/10.1016/j.entcs.2020.09.012
  serial-number:
    doi: 10.1016/j.entcs.2020.09.012
    issn: 1571-0661
  parent:
    type: periodical
    title: Electronic Notes in Theoretical Computer Science
    publisher: Elsevier BV
    volume: 352

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Cited by (2)

Proof Theory of Partially Normal Skew Monoidal Categories uustalu-2021-proofEPTCS · 2021

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Deductive Systems and Coherence for Skew Prounital Closed Categories uustalu-2021-deductiveEPTCS · 2021

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Cites 34 works (4 here)

With notes (4)

Proof Theory of Partially Normal Skew Monoidal Categories uustalu-2021-proofEPTCS · 2021

DOI · arXiv

A sequent calculus for a semi-associative law zeilberger-2019-aLMCS · 2019

We introduce a sequent calculus with a simple restriction of Lambek’s product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice

𝑌_{𝑛}

DOI · arXiv

A theory of linear typings as flows on 3-valent graphs zeilberger-2018-aLICS · 2018

DOI · arXiv

The mathematics of sentence structure lambek58Amer. Math. Monthly · 1958

DOI

External (30)

Braided skew monoidal categories (2020)
Free skew monoidal categories (2018)
Skew monoidal categories and skew multicategories (2018)
The sequent calculus of skew monoidal categories (2018)
Monads need not be endofunctors (2015)
The Catalan simplicial set (2014)
Triangulations, orientals, and skew monoidal categories (2014)
Coherence for skew-monoidal categories (2014)
Skew-closed categories (2013)
Skew monoidales, skew warpings and quantum categories (2012)
Skew-monoidal categories and bialgebroids (2012)
Closed categories (nLab) (2009)
Premonoidal categories and notions of computation (1997)
Full intuitionistic linear logic (extended abstract) (1993)
Embedding closed categories (1978)
Categories for the Working Mathematician (2nd ed.) (1978)
A note on monoidal monads (1977)
Coherence in nonmonoidal closed categories (1977)
Embedding of closed categories into monoidal closed categories (1977)
Algebraic Theories (1976)
Symmetric closed categories (1975)
On closed categories of functors II (1974)
An embedding theorem for closed categories (1974)
Coherence for associativity not an isomorphism (1972)
Coherence in closed categories (1971)
On closed categories of functors (1970)
Closed categories (1966)
On MacLane's conditions for coherence of natural associativities, commutativities, etc (1964)
Catégories avec multiplication (1963)
Natural associativity and commutativity (1963)