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Graph homotopy and Graham homotopy

open access: yesDiscrete Mathematics, 2001
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Yeong-Nan Yeh   +2 more
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Homotopy-epimorphisms, homotopy-monomorphisms and homotopy-equivalences

open access: yesTopology and Its Applications, 1992
In a general category, a morphism which is both an epimorphism and a monomorphism need not be an equivalence. However, the authors prove that it is in the case of the homotopy category of pointed path-connected CW-spaces. In fact, they obtain this result as a corollary of a variant of a classical theorem of J. H. C. Whitehead that they prove. They also
Dyer, Eldon, Roitberg, Joseph
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A Note On Homotopy Pushout And Homotopy Coherence

Quaestiones Mathematicae, 2003
We present a self-contained argument, characterizing a homotopy pushout square by recognizing it as an initial object in a certain coherent homotopy category of spaces under a cotriad. Mathematics Subject Classification (2000): 18A30, 55P10, 55Q05.
Hardie, K.A., Kamps, K.H., Witbooi, P.J.
openaire   +2 more sources

Homotopy epimorphisms in homotopy pullbacks

open access: yesTopology and Its Applications, 1994
The authors prove that homotopy epimorphisms are preserved under homotopy pullback. (A map \(f: X\to Y\) of pointed path-connected CW-spaces is a homotopy epimorphism, if given \(u,v: Y\to Z\), \(u\circ f\simeq v\circ f\) implies \(u\simeq v\).) The proof makes use of \textit{M. Mather}'s first cube theorem [Can. J. Math.
Hong, Lin, Wenhuai, Shen
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