# Contractible simplicial objects

Michael Barr; John F. Kennison; Robert M. Raphael

Commentationes Mathematicae Universitatis Carolinae (2019)

- Volume: 60, Issue: 4, page 473-495
- ISSN: 0010-2628

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topBarr, Michael, Kennison, John F., and Raphael, Robert M.. "Contractible simplicial objects." Commentationes Mathematicae Universitatis Carolinae 60.4 (2019): 473-495. <http://eudml.org/doc/295068>.

@article{Barr2019,

abstract = {We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by $-1$, which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy implies extra degeneracy implies homotopic to a constant and give explicit examples to show the converses fail.},

author = {Barr, Michael, Kennison, John F., Raphael, Robert M.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {contractible; homotopic to a constant; reduced homotopy; partial simplicial object},

language = {eng},

number = {4},

pages = {473-495},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Contractible simplicial objects},

url = {http://eudml.org/doc/295068},

volume = {60},

year = {2019},

}

TY - JOUR

AU - Barr, Michael

AU - Kennison, John F.

AU - Raphael, Robert M.

TI - Contractible simplicial objects

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2019

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 60

IS - 4

SP - 473

EP - 495

AB - We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by $-1$, which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy implies extra degeneracy implies homotopic to a constant and give explicit examples to show the converses fail.

LA - eng

KW - contractible; homotopic to a constant; reduced homotopy; partial simplicial object

UR - http://eudml.org/doc/295068

ER -

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