TL;DR
This paper extends Kelly's internal Hom construction for enriched categories to lax functors valued in symmetric monoidal categories, establishing a foundation for a calculus on lax functors.
Contribution
It introduces a calculus on lax functors by generalizing the internal Hom construction to lax functors in symmetric monoidal categories.
Findings
Extended Kelly's construction to lax functors
Established a framework for weakly enriched categories
Provided tools for lax diagram analysis
Abstract
We verify that Kelly's constructions of the internal Hom for enriched categories extends naturally to lax functors taking their values in a symmetric monoidal category. Our motivation is to set up a `calculus on lax functors' that will host the theory of weakly enriched categories that are defined by lax diagrams.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra