A note on Frobenius monoidal functors on autonomous categories
Adriana Balan
TL;DR
This paper explores the relationship between Frobenius monoidal functors and dual-preserving (co)monoidal functors in autonomous categories, establishing a converse connection and applying it to linearly distributive functors.
Contribution
It proves that dual-preserving (co)monoidal functors between autonomous categories are Frobenius monoidal, providing a new characterization and applying it to linearly distributive functors.
Findings
Dual-preserving (co)monoidal functors are Frobenius monoidal.
Established a converse relationship in autonomous categories.
Applied results to linearly distributive functors.
Abstract
Frobenius monoidal functors preserve duals. We show that conversely, (co)monoidal functors between autonomous categories which preserve duals are Frobenius monoidal. We apply this result to linearly distributive functors between autonomous categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory