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removed the word "finally" in "finally established".
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Urs Schreiber
Urs Schreiber
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re 1: Yes.

Recently the equivalence between the Jacob Lurie's model for infinity-operads via "$\infty$-categories of operators" and Ieke Moerdijk's model (together with D.-C. Cisinski based on work of Weiss) in terms of dendroidal sets was finally established, in

  • Gijs Heuts, Vladimir Hinich, Ieke Moerdijk, The equivalence between Lurie's model and the dendroidal model for infinity-operads (arXiv:1305.3658) .

Via the previously established equivalences of the model structure on dendroidal sets with various other models for homotopy operads, notably its equivalence to the model structure on simplicial operads this now also shows that Jacob Lurie's definition is equivalent to all these.

re 1: Yes.

Recently the equivalence between the Jacob Lurie's model for infinity-operads via "$\infty$-categories of operators" and Ieke Moerdijk's model (together with D.-C. Cisinski based on work of Weiss) in terms of dendroidal sets was finally established, in

  • Gijs Heuts, Vladimir Hinich, Ieke Moerdijk, The equivalence between Lurie's model and the dendroidal model for infinity-operads (arXiv:1305.3658) .

Via the previously established equivalences of the model structure on dendroidal sets with various other models for homotopy operads, notably its equivalence to the model structure on simplicial operads this now also shows that Jacob Lurie's definition is equivalent to all these.

re 1: Yes.

Recently the equivalence between the Jacob Lurie's model for infinity-operads via "$\infty$-categories of operators" and Ieke Moerdijk's model (together with D.-C. Cisinski based on work of Weiss) in terms of dendroidal sets was established, in

  • Gijs Heuts, Vladimir Hinich, Ieke Moerdijk, The equivalence between Lurie's model and the dendroidal model for infinity-operads (arXiv:1305.3658) .

Via the previously established equivalences of the model structure on dendroidal sets with various other models for homotopy operads, notably its equivalence to the model structure on simplicial operads this now also shows that Jacob Lurie's definition is equivalent to all these.

Source Link
Urs Schreiber
Urs Schreiber
  • 19.8k
  • 1
  • 74
  • 269

re 1: Yes.

Recently the equivalence between the Jacob Lurie's model for infinity-operads via "$\infty$-categories of operators" and Ieke Moerdijk's model (together with D.-C. Cisinski based on work of Weiss) in terms of dendroidal sets was finally established, in

  • Gijs Heuts, Vladimir Hinich, Ieke Moerdijk, The equivalence between Lurie's model and the dendroidal model for infinity-operads (arXiv:1305.3658) .

Via the previously established equivalences of the model structure on dendroidal sets with various other models for homotopy operads, notably its equivalence to the model structure on simplicial operads this now also shows that Jacob Lurie's definition is equivalent to all these.