On homotopy varieties

Details On homotopy varieties On homotopy varieties

2005-09-28

arxiv.org/abs/math/0509655v2

Mathematics

Category Theory

Proposition 4.5 is not valid; see Remark 4.5(e) in the new version. All other results are correct but there are gaps in proofs

Scientific paper

Given an algebraic theory $\ct$, a homotopy $\ct$-algebra is a simplicial set where all equations from $\ct$ hold up to homotopy. All homotopy $\ct$-algebras form a homotopy variety. We give a characterization of homotopy varieties analogous to the characterization of varieties. We will also study homotopy models of limit theories which leads to homotopy locally presentable categories. These were recently considered by Simpson, Lurie, To\"{e}n and Vezzosi.

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