11 февр. 2020 г. · As a form of ur-witticism, we shall adopt the term ∞-cosmology for the form of synthetic ∞-category theory presented in these lectures.

We propose foundations for a synthetic theory of (∞,1)-categories within homotopy type theory. We axiomatize a directed interval type, then define higher ...

14 окт. 2023 г. · Consequently, formal ( ∞ , 1 ) (\infty,1) -category theory has also been called synthetic ( ∞ , 1 ) (\infty,1) -category theory. 2. Approaches.

1 сент. 2024 г. · Synthetic category theory is an approach to the foundation of mathematics in which the principal objects are ∞-categories. The theory is due to ...

7 окт. 2024 г. · In “synthetic” approaches to the formulation of theories in mathematics the emphasis is on axioms that directly capture the core aspects of the intended ...

11 июл. 2022 г. · However, doing (∞,1)-category theory synthetically in standard HoTT has remained an open problem. In this talk, I present such a development in ...

21 мая 2017 г. · We propose foundations for a synthetic theory of (\infty,1)-categories within homotopy type theory. We axiomatize a directed interval type, then define higher ...

4 мая 2021 г. · We study cocartesian fibrations in the setting of the synthetic (\infty,1)-category theory developed in the simplicial type theory introduced by Riehl and ...

1 мар. 2018 г. · Homotopy type theory provides a “synthetic” framework that is suitable for developing the theory of mathematical objects with natively.

Pioneered by Voevodsky, this logical system is designed to develop homotopy theory in a synthetic way, meaning that its basic entities can essentially be ...