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 -
References
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