Constructing Coproducts in locally Cartesian closed $\infty$-Categories

TL;DR

This paper proves that in certain advanced mathematical categories, the existence of a subobject classifier guarantees the presence of initial objects and specific coproducts, enriching the structural understanding of these categories.

Contribution

It establishes that locally Cartesian closed ∞-categories with subobject classifiers necessarily have strict initial objects and disjoint, universal binary coproducts, advancing categorical theory.

Findings

Existence of strict initial objects in these categories

Presence of disjoint, universal binary coproducts

Structural implications for ∞-categories with subobject classifiers

Abstract

We prove that every locally Cartesian closed $\infty$-category with subobject classifier has a strict initial object and disjoint and universal binary coproducts.