Canadian Journal of Mathematics · 1976 · 178 citations · 5 references
Natural SciencesMathematicsDescriptive GeometryDwelling TheoryTopologyCategory TheoryCohomology TheoryHomotopy TheoryBased HomotopyHomotopy Classes Of MapsHomotopy Theoretic Category Theory
In the based homotopy category pull‑backs and push‑outs generally fail to exist, as shown by the lack of kernels for essential maps between Eilenberg‑MacLane spaces of different dimensions. The authors introduce homotopy pull‑backs and push‑outs that exist in this category and possess properties analogous to classical pull‑backs and push‑outs. They construct these homotopy pull‑backs and push‑outs using standard homotopical techniques and verify their universal properties. The paper illustrates applications of these constructions in several contexts, as cited in references 3, 5, 6, and 14.
The (based) homotopy category consists of (based) topological spaces and (based) homotopy classes of maps. In these categories, pull-backs and push-outs do not generally exist. For example, no essential map between Eilenberg-MacLane spaces of different dimensions has a kernel. In this paper we define homotopy pull-backs and push-outs, which do exist and which behave like pull-backs and push-outs, and we give some of their properties. Applications may be found in [ 3 ; 5 ; 6 and 14 ].
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Partitions of Unity in the Theory of Fibrations
Albrecht Dold · Annals of Mathematics · 1963 · 380 citations
Edwin H. Spanier, J. H. C. Whitehead · Mathematika · 1955 · 82 citations
Yasutoshi Nomura · Osaka City University (Osaka City University) · 1970 · 15 citations · Full text