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A new approach to model categorical homotopy fiber sequences

Volume 581 / 2022

Alisa Govzmann, Damjan Pištalo, Norbert Poncin Dissertationes Mathematicae 581 (2022), 1-57 MSC: Primary 18E35; Secondary 18N40, 14A30. DOI: 10.4064/dm858-5-2022 Published online: 9 July 2022

Abstract

We propose a simplified definition of Quillen’s fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding that the homotopy theory of the model category’s arrow category contains all homotopical information about its long fibration sequences.

Authors

  • Alisa GovzmannFaculty of Science, Technology, and Medicine
    University of Luxembourg
    6, Avenue de la Fonte
    L-4364 Esch-sur-Alzette, Luxembourg
    e-mail
  • Damjan PištaloFaculty of Science, Technology, and Medicine
    University of Luxembourg
    6, Avenue de la Fonte
    L-4364 Esch-sur-Alzette, Luxembourg
    e-mail
  • Norbert PoncinFaculty of Science, Technology, and Medicine
    University of Luxembourg
    6, Avenue de la Fonte
    L-4364 Esch-sur-Alzette, Luxembourg
    e-mail

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