In mathematics, Kan complexes and Kan fibrations are part of the theory of simplicial sets. Kan fibrations are the fibrations of the standard model category structure on simplicial sets and are therefore of fundamental importance. Kan complexes are the fibrant objects in this model category. The name is in honor of Daniel Kan.
In mathematics, Kan complexes and Kanfibrations are part of the theory of simplicial sets. Kanfibrations are the fibrations of the standard model category...
Daniel Marinus Kan (or simply Dan Kan) (August 4, 1927 – August 4, 2013) was a Dutch mathematician working in category theory and homotopy theory. He was...
point of the theory is that the geometric realization of a Kanfibration is a Serre fibration of spaces. With the model structure in place, a homotopy theory...
universal fibration was univalent: the associated fibration of pairwise homotopy equivalences between the fibers is equivalent to the paths-space fibration of...
of a model category M, a fibrant object A of M is an object that has a fibration to the terminal object of the category. The fibrant objects of a closed...
pointed finite sets) to C provided C is pointed. op-fibration A functor π:C → D is an op-fibration if, for each object x in C and each morphism g : π(x)...
{\displaystyle [0,1]} .) This definition is formally dual to that of a fibration, which is required to satisfy the homotopy lifting property with respect...
implicit. A fibration in the sense of Serre is the dual notion of a cofibration: that is, a map p : X → B {\displaystyle p:X\to B} is a fibration if given...
referred to below makes analogies between these ideas and the notion of fibration of spaces. These ideas simplify in the case of groupoids, as shown in...
A fiber laser (or fibre laser in Commonwealth English) is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such...
categories fibrations and cofibrations are independent and that for an ABC model category MD is an ABC model category. To an ABC (co)fibration category...
subject to the following axioms. A fibration that is also a weak equivalence is called an acyclic (or trivial) fibration and a cofibration that is also a...
Dold–Thom theorem, the Dold–Kan correspondence, and introduced Dold manifolds, Dold–Puppe stabilization, and Dold fibrations. Albrecht Dold was born in...
high-fire-risk applications, such as firefighting and front-line combat. Kan, Chi-wai; Yam, Lim-yung; Ng, Sun-pui (2013-10-31). "The Effect of Stretching...
Kabushiki gaisha 日本電信電話株式会社等に関する法律, Nippon Denshin Denwa kabushiki gaisha-tō ni kan-suru hōritsu, Law No. 85 of December 25, 1984 "NTT Group Website". Nippon...
25, 2017. Hack, Rachel (September 3, 2013). "Rolling into Roeland Park, Kan". Official Google Fiber Blog. Archived from the original on November 12,...
homotopy inverse. Analysis Situs approximate fibration 1. An approximate fibration, a generalization of a fibration and a projection in a locally trivial bundle...
zienswijze ook op andere (doeltreffender) wijze en met betere bewoordingen kan illustreren. In doing so, within the framework of the exaggeration permitted...
defeat against the Northern Wei. They ousted the local Gaochang governor Kan Shuang (闞爽) who escaped to the Rouran Khaganate, and they established the...
Knopf Doubleday Publishing Group. p. 286. ISBN 9780307962256. Tu, Karen Kan-Lun (2017). Wa and Tatala: The Transformation of Indigenous Canoes on Yap...
CD003132. doi:10.1002/14651858.CD003132.pub2. PMID 20091539. Wu Y, Zhu S, Lv Z, Kan S, Wu Q, Song W, et al. (December 2019). "Effects of therapeutic ultrasound...
sequence for the singular cohomology of the pullback of a fibration Serre spectral sequence of a fibration Adams spectral sequence in stable homotopy theory Adams–Novikov...
elaborated at Lattice of covering groups. Fibrations provide a very powerful means to compute homotopy groups. A fibration f the so-called total space, and the...
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