The price to pay to access this structure is to enhance sets into ∞-groupoids. Bye bye sets…

This is a big revolution, a shift of paradigm.

Toën, B. 2014. ‘Derived Algebraic Geometry,’ arXiv:1401.1044.

the expression homotopical mathematics reflects a shift of paradigm in which the relation of equality relation is weakened to that of homotopy. (Toën 2014, p. 3)

At the same time, he points the reader to the HoTT program as the new foundational language for this homotopical mathematics.

Also Preface of Denis-Charles Cisinski’s Higher Categories and Homotopical Algebra. (‘A glimpse at the narrative’)

Created on May 18, 2020 at 03:15:16.
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