Examples of para-cocyclic objects induced by BD-laws

TL;DR

This paper extends the construction of para-cocyclic objects from algebra homomorphisms to more general locally braided morphisms of monads, broadening the scope of the original framework.

Contribution

It introduces new examples of admissible septuples derived from locally braided morphisms of monads, expanding the applicability of para-cocyclic structures.

Findings

Generalizes para-cocyclic constructions beyond algebra homomorphisms

Provides new examples using locally braided morphisms of monads

Enhances understanding of admissible septuples in categorical contexts

Abstract

In a recent paper arXiv:0705.3190, we gave a general construction of a para-cocyclic structure on a cosimplex, associated to a so called admissible septuple -- consisting of two categories, three functors and two natural transformations, subject to compatibility relations. The main examples of such admissible septuples were induced by algebra homomorphisms. In this note we provide more general examples coming from appropriate (`locally braided') morphisms of monads.