Geodesic
Enriched Orthogonality and Equivalences
Theory and applications of categories, Tome 22 (2009), pp. 302-312 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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In this paper, we consider an enriched orthogonality for classes of spaces, with respect to groupoids, simplicial sets and spaces themselves. This point of view allows one to characterize homotopy equivalences, shape and strong shape equivalences. We show that there exists a class of spaces, properly containing ANR-spaces, for which shape and strong shape equivalences coincide. For such a class of spaces homotopy orthogonality implies enriched orthogonality.

Classification : 55P10, 55P15, 55P5
Keywords: ANR-space, enriched orthogonality, groupoid, homotopy structure, prospace, shape equivalence, simplicial set, ${\mathcal V}$-orthogonal object, strongly fibered space 
@article{TAC_2009_22_a10,
     author = {M. Golasinski and L. Stramaccia},
     title = {Enriched {Orthogonality} and {Equivalences}},
     journal = {Theory and applications of categories},
     pages = {302--312},
     year = {2009},
     volume = {22},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a10/}
}
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M. Golasinski; L. Stramaccia. Enriched Orthogonality and Equivalences. Theory and applications of categories, Tome 22 (2009), pp. 302-312. http://geodesic.mathdoc.fr/item/TAC_2009_22_a10/