On local presentability of T/A

TL;DR

This paper proves that under certain conditions, the comma category of a locally presentable category with a lambda-accessible functor remains locally presentable, extending the understanding of categorical structures.

Contribution

It establishes that the comma category T/𝒜 is locally λ-presentable when 𝒜 is locally λ-presentable and T is λ-accessible, providing a new structural insight.

Findings

T/𝒜 is locally λ-presentable under given conditions

Extends properties of locally presentable categories to comma categories

Supports further categorical constructions involving accessible functors

Abstract

We prove that if $\mathcal{A}$ is a locally $\lambda$-presentable category and $T : \mathcal{A} \to \mathcal{A}$ is a $\lambda$-accessible functor then $T/\mathcal{A}$ is locally $\lambda$-presentable.