Homotopical algebra in homotopical categories

  title={Homotopical algebra in homotopical categories},
  author={Marco Grandis},
  journal={Applied Categorical Structures},
Abstract. We develop here a version of abstract homotopical algebra based on homotopy kernels and cokernels, which are particular homotopy limits and colimits. These notions are introduced in an h-category, a sort of two-dimensional context more general than a 2-category, abstracting the nearly 2-categorical properties of topological spaces, continuous maps and homotopies. A setting which applies also, at different extents, to cubical or simplicial sets, chain complexes, chain algebras .... and… CONTINUE READING

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