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Minimal fibrations of dendroidal sets. (English) Zbl 1383.55012

Minimal fibrations in the theory of simplicial sets provide for very rigid models of maps, rendering them particularly useful for various constructions. By a result of D.-C. Cisinski [“Univalent universes for elegant models of homotopy types”, Preprint, arXiv:1406.0058], the classical construction of minimal fibrations is a special case of the existence of minimal fibrations in a model structure of suitable Reedy diagrams. The authors show that the classical minimal fibration replacement construction extends from simplicial sets to dendroidal sets. The passage from the simplicial category \(\Delta\) to the dendroidal category \(\Omega\) involves, as usual, quite a significant refinement of classical arguments. The presentation is given in such a way that the construction immediately implies the result in the context of suitable generalised Reedy diagrams.

MSC:

55R65 Generalizations of fiber spaces and bundles in algebraic topology
55U35 Abstract and axiomatic homotopy theory in algebraic topology
55P48 Loop space machines and operads in algebraic topology
18D50 Operads (MSC2010)
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