Enriched coverages and sheaves under change of base

TL;DR

This paper studies how changing the base category in enriched category theory affects coverages and sheaves, showing injectivity properties and conditions for commutation of sheaf construction with base change.

Contribution

It establishes injectivity of subobjects and coverages under base change and identifies conditions for the sheaf construction to commute with base change.

Findings

Base change induces injective mappings on subobjects and coverages.

Full base change functors ensure sheaf construction commutes with base change.

Results deepen understanding of enriched sheaf theory under base change.

Abstract

We investigate how change of enriching base category via a faithful, conservative right adjoint functor interacts with enriched coverages and sheaves on a given enriched category. We prove that change of base via such a functor gives rise both to an injective mapping on subobjects in enriched presheaf categories, and to an injective mapping on enriched coverages. In case the base change functor is also full, the enriched associated sheaf construction on a presheaf category commutes with base change.