Homotopy cartesian squares in extriangulated categories

Jing He; Chenbei Xie; Panyue Zhou

Homotopy cartesian squares in extriangulated categories

Representation Theory 2022-06-24 v1 Category Theory

Authors: Jing He , Chenbei Xie , Panyue Zhou

Abstract

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category. Given a composition of two commutative squares in $\mathcal{C}$ , if two commutative squares are homotopy cartesian, then their composition is also a homotopy cartesian. This covers the result by Mac Lane (1998) for abelian categories and the result by Christensen and Frankland (2022) for triangulated categories.

Keywords

homotopy theory triangulated categories homotopy groups

Cite

@article{arxiv.2206.11429,
  title  = {Homotopy cartesian squares in extriangulated categories},
  author = {Jing He and Chenbei Xie and Panyue Zhou},
  journal= {arXiv preprint arXiv:2206.11429},
  year   = {2022}
}

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8 pages

Homotopy cartesian squares in extriangulated categories

Abstract

Keywords

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