Exactness and stability in homotopical algebra
代数拓扑
2016-09-07 v1 范畴论
摘要
Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be given for very general 'categories with homotopies' having homotopy kernels and cokernels, but become more interesting under suitable stability hypotheses, satisfied - in particular - by chain complexes. It is then possible to measure the default of homotopical exactness of a sequence by the homotopy type of a certain object, a sort of 'homotopical homology'.
引用
@article{arxiv.math/0008236,
title = {Exactness and stability in homotopical algebra},
author = {Marco Grandis},
journal= {arXiv preprint arXiv:math/0008236},
year = {2016}
}
备注
24 pages