Solving Homotopy Domain Equations

TL;DR

This paper introduces a general technique for solving domain equations in cartesian closed ∞-categories to construct homotopy λ-models with rich ∞-groupoid structures, and demonstrates its application with examples.

Contribution

It develops a novel method for solving domain equations in ∞-categories, enabling the construction of homotopy λ-models with complex higher-groupoid structures.

Findings

A general technique for solving domain equations in c.c.i. categories.

Construction of homotopy λ-models with ∞-groupoid structures.

Examples demonstrating the application of the technique.

Abstract

In order to get $\lambda$-models with a rich structure of $\infty$-groupoid, which we call "homotopy $\lambda$-models", a general technique is described for solving domain equations on any cartesian closed $\infty$-category (c.c.i.) with enough points. Finally, the technique is applied in a particular c.c.i., where some examples of homotopy $\lambda$-models are given.