Abstract:
Operads provide a unifying language for describing compositional and hierarchical structures across a broad spectrum of mathematical contexts. This talk offers a concise historical overview of operads and introduces their formal definition, emphasizing their structural composition rules and inherent symmetries governed by permutation actions. We begin by demonstrating that the species of cycles naturally forms an operad. Extending beyond earlier studies, which focus solely on the operadic structure in the first entry, we present new results showing that the species of posets also forms an operad in the second entry. Letting L denote the category of linear orders, we prove that for any poset Q, the undercategory Q/L admits an operadic structure. The central theorem introduces the operadic composition on the category of finite posets P, defined via the lexicographic sum. It is shown that for every poset Q, the undercategory Q/P likewise supports an operad structure. This exposition combines foundational theory with recent advances, offering insights into the flexibility of operads and their role in organizing combinatorial data via species.
Page(s):
36-36
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025