The fundamental groupoid as a terminal costack

Ilia Pirashvili

The fundamental groupoid as a terminal costack

Algebraic Topology 2014-06-18 v1

Authors: Ilia Pirashvili

Abstract

Let $X$ be a topological space. We denote by $\pi_0(X)$ the set of connected components of $X$ and by $\Pi_1(U)$ the fundamental groupoid. In this paper we prove that for good topological spaces the assignments $U\mapsto\pi_0(U)$ and $U\mapsto\Pi_1(U)$ are the terminal cosheaf and costack respectively.

Cite

@article{arxiv.1406.4419,
  title  = {The fundamental groupoid as a terminal costack},
  author = {Ilia Pirashvili},
  journal= {arXiv preprint arXiv:1406.4419},
  year   = {2014}
}

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