Directed fibrations and covering projections
Copyright policy )Directed fibrations and covering projections
Summary: In this note a notion of Hurewicz fibration in the category d{\textbf{Top}} of directed spaces in the sense of \textit{M. Grandis} [Cah. Topol. Géom. Différ. Catég. 44, No.~4, 281--316 (2003; Zbl 1059.55009)] is defined. The directed homotopy lifting property is characterized by means of lifting pairs. The unique lifting property for directed paths and loops is studied. Relations with the fundamental category and the fundamental monoid are established. In this context, a notion of a directed covering projection is also studied and some relations of this notion with the dicovering spaces of \textit{L. Fajstrup} [Homology Homotopy Appl. 5, No.~2, 1--17 (2003; Zbl 1030.68057)] are established.
directed covering projection, directed cellular complexes, Fiber spaces in algebraic topology, unique directed path (loop) lifting, lifting pair, dicovering spaces, Topological spaces with richer structures, fundamental category (monoid), directed homotopy lifting property, Covering spaces and low-dimensional topology
directed covering projection, directed cellular complexes, Fiber spaces in algebraic topology, unique directed path (loop) lifting, lifting pair, dicovering spaces, Topological spaces with richer structures, fundamental category (monoid), directed homotopy lifting property, Covering spaces and low-dimensional topology
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