Path categories and quasi-categories
J.F. Jardine

TL;DR
This paper introduces the homotopy theory of quasi-categories, characterizing weak equivalences via induced equivalences on associated groupoids, which serve as higher homotopy group analogs.
Contribution
It provides a foundational framework for understanding homotopy theory in quasi-categories using groupoids to replace higher homotopy groups.
Findings
Weak equivalences characterized by induced equivalences on groupoids
Groupoids effectively replace higher homotopy groups in quasi-category theory
Establishes a foundational approach to quasi-category homotopy theory
Abstract
This paper gives an introduction to the homotopy theory of quasi-categories. Weak equivalences between quasi-categories are characterized as maps which induce equivalences on a naturally defined system of groupoids. These groupoids effectively replace higher homotopy groups in quasi-category homotopy theory.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
