Pith. sign in

REVIEW 3 cited by

Cofibrations in Homotopy Theory

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0610009 v4 pith:UIWXWLBF submitted 2006-09-30 math.AT math.KT

Andrei Radulescu-Banu This is my paper · ORCID
classification math.ATmath.KT
keywords categorieshomotopycofibrationtheorycolimitsfibrationhelleranderson-brown-cisinski
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Homotopy theories via the magnitude-path spectral sequence

    math.AT 2026-06 unverdicted novelty 7.0 of 10

    Defines r-quasi-isomorphisms and r-cofibrations on generalized metric spaces so that each page of the magnitude-path spectral sequence satisfies metric Eilenberg-Steenrod axioms and supports Brown category structures ...

  2. Generalized inverse diagrams in tribes

    math.CT 2026-02 conditional novelty 6.0 of 10

    A new 'unrolling' construction turns generalized Reedy categories into strict ones, yielding tribe structures on fibrant diagram categories over generalized inverse categories.

  3. Pushforwards in Inverse Homotopical Diagrams

    math.CT 2025-06 conditional novelty 6.0 of 10

    If every weak equivalence out of an index object is either initial among the maps out of it, or all maps out of it are weak equivalences, then homotopical inverse diagrams are closed under pushforwards along Reedy fibrations.

Pith tools