# A standard theorem on adjunctions in two variables

## TL;DR

This paper provides an explicit proof of a theorem that extends a two-variable adjunction to the arrow categories of its domains, clarifying how adjunctions behave in more complex categorical structures.

## Contribution

It offers a detailed proof of a known theorem, enhancing understanding of how two-variable adjunctions lift to arrow categories.

## Key findings

- Explicit proof of the adjunction lifting theorem
- Clarification of adjunction behavior in arrow categories
- Improved understanding of two-variable adjunctions

## Abstract

We record an explicit proof of the theorem that lifts a two-variable adjunction to the arrow categories of its domains.