Homotopy dimension

In mathematics, especially algebraic topology, the homotopy dimension of a topological space does not have a fixed meaning. However, it can refer to

• the minimum dimension of a CW complex that is homotopy equivalent to the space.
• the Lebesgue covering dimension of the space
• homotopy dimension introduced by Lurie in his Higher Topos Theory for an ∞-topos.

• https://mathoverflow.net/questions/232558/dimension-of-a-homotopy-type
• https://mathoverflow.net/questions/56889/homotopy-dimension-of-a-mapping
• http://pantodon.jp/index.rb?body=dimension_theory in Japanese
• https://ncatlab.org/nlab/show/homotopy+dimension (this article is about homotopy dimension in Lurie' higher topos theory)

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