Pith. sign in

REVIEW 1 cited by

Fibrations and homotopy colimits of simplicial sheaves

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/9811038 v2 pith:LXRE5Y43 submitted 1998-11-06 math.AT math.CT

Charles Rezk This is my paper · ORCID
classification math.ATmath.CT
keywords homotopysheavessimplicialcolimitsnotionspacesadditionanalogous
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the notion of a quasi-fibration of spaces, and seems to be of independent interest.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Internal Algebraic Type Theory

    math.CT 2026-07 conditional novelty 7.0 of 10

    Maps that are exponentiable with respect to a family of maps give polynomial functors and an algebraic model of directed type theory in the category of categories with hom-types.

Pith tools