Cofibrations in Homotopy Theory
By Andrei Radulescu-Banu. 2006
68 citations recorded by the source corpus.
We define Anderson-Brown-Cisinski (ABC) cofibration categories, and construct homotopy colimits of diagrams of objects in ABC cofibration categories. Homotopy colimits for Quillen model categories are obtained as a particular case. We attach to each ABC cofibration category a left Heller derivator. A dual theory is developed for homotopy limits in ABC fibration categories and for right Heller derivators. These constructions provide a natural framework for 'doing homotopy theory' in ABC (co)fibration categories.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4da763aa2b5f1820d3f90ff1c0c0460aa30a7201
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In Algebra and Number Theory
- Andrew Justin Blumberg
- Yonatan Harpaz
- Ilan Barnea
- Michael A. Mandell
- Geoffroy Horel
- Clark Barwick
- John E. Harper
- A. Lazarev
In Geometry and Topology
- Andrew Justin Blumberg
- Yonatan Harpaz
- Ilan Barnea
- Michael A. Mandell
- Geoffroy Horel
- Clark Barwick
- D. Gepner
- Gonçalo Tabuada
In Mathematical Physics
- Andrew Justin Blumberg
- Yonatan Harpaz
- Ilan Barnea
- Michael A. Mandell
- Geoffroy Horel
- Clark Barwick
- D. Gepner
- Gonçalo Tabuada
Citations in the corpus
- Pro-categories in homotopy theory (2015, background): “1 were intensively studied by Anderson, Brown, Cisinski and others (see [An78],[Ci10b],[RB06] and[Sz14]).”
- The homotopy theory of cyclotomic spectra (2013, background): “These limits and colimits suffice to construct the entirety of the homotopy theory set up in Chapter I of Quillen [12] and much of the abstract homotopy theory developed since; e.g., see Radulescu-Banu [13], where this is worked out in even greater generality.”