
TL;DR
This paper introduces generalized nerve constructions for monads that extend the Kleisli construction, providing fully faithful 2-functors from monads to double categories, enriching the categorical understanding of monads.
Contribution
It develops more general nerve constructions on 2-categories of monads, expanding the classical Kleisli-based approach with new fully faithful 2-functors.
Findings
New nerve constructions for monads are fully faithful.
These constructions generalize the Kleisli nerve.
They establish a richer categorical framework for monads.
Abstract
One interpretation of the Kleisli construction (given by Miranda and related to work of Par\'e) is as a nerve sending a monad to the Kleisli double category of . In this paper we find more general nerve constructions on the 2-categories of monads, which also give fully faithful nerve 2-functors .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Intracranial Aneurysms: Treatment and Complications
