NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES

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NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES. / Kock, Joachim.

In: Journal of Homotopy and Related Structures, Vol. 2, No. 2, 2007, p. 217-228.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kock, J 2007, 'NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES', Journal of Homotopy and Related Structures, vol. 2, no. 2, pp. 217-228.

APA

Kock, J. (2007). NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES. Journal of Homotopy and Related Structures, 2(2), 217-228.

Vancouver

Kock J. NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES. Journal of Homotopy and Related Structures. 2007;2(2):217-228.

Author

Kock, Joachim. / NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES. In: Journal of Homotopy and Related Structures. 2007 ; Vol. 2, No. 2. pp. 217-228.

Bibtex

@article{fa9c791b918749b496fe2669982bbd86,
title = "NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES",
abstract = "A concrete computation - twelve slidings with sixteen tiles - reveals that certain commutativity phenomena occur in every double semigroup. This can be seen as a sort of Eckmann-Hilton argument, but it does not use units. The result implies in particular that all cancellative double semigroups and all inverse double semigroups are commutative. Stepping up one dimension, the result is used to prove that all strictly associative two-fold monoidal categories (with weak units) are degenerate symmetric. In particular, strictly associative one-object, one-arrow 3-groupoids (with weak units) cannot realise all simply-connected homotopy 3-types.",
keywords = "Double semigroups, commutativity, units, two-fold monoidal categories",
author = "Joachim Kock",
year = "2007",
language = "English",
volume = "2",
pages = "217--228",
journal = "Journal of Homotopy and Related Structures",
issn = "2193-8407",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES

AU - Kock, Joachim

PY - 2007

Y1 - 2007

N2 - A concrete computation - twelve slidings with sixteen tiles - reveals that certain commutativity phenomena occur in every double semigroup. This can be seen as a sort of Eckmann-Hilton argument, but it does not use units. The result implies in particular that all cancellative double semigroups and all inverse double semigroups are commutative. Stepping up one dimension, the result is used to prove that all strictly associative two-fold monoidal categories (with weak units) are degenerate symmetric. In particular, strictly associative one-object, one-arrow 3-groupoids (with weak units) cannot realise all simply-connected homotopy 3-types.

AB - A concrete computation - twelve slidings with sixteen tiles - reveals that certain commutativity phenomena occur in every double semigroup. This can be seen as a sort of Eckmann-Hilton argument, but it does not use units. The result implies in particular that all cancellative double semigroups and all inverse double semigroups are commutative. Stepping up one dimension, the result is used to prove that all strictly associative two-fold monoidal categories (with weak units) are degenerate symmetric. In particular, strictly associative one-object, one-arrow 3-groupoids (with weak units) cannot realise all simply-connected homotopy 3-types.

KW - Double semigroups

KW - commutativity

KW - units

KW - two-fold monoidal categories

M3 - Journal article

VL - 2

SP - 217

EP - 228

JO - Journal of Homotopy and Related Structures

JF - Journal of Homotopy and Related Structures

SN - 2193-8407

IS - 2

ER -

ID: 331502452