Gr\"obner-Shirshov bases for categories
L. A. Bokut, Yuqun Chen, Yu Li
TL;DR
This paper develops a Composition-Diamond lemma for small categories and constructs Gr"obner-Shirshov bases for specific categories like simplicial and cyclic categories.
Contribution
It introduces a new theoretical framework for categories using Gr"obner-Shirshov bases and applies it to important categorical structures.
Findings
Established Composition-Diamond lemma for small categories
Constructed Gr"obner-Shirshov bases for simplicial and cyclic categories
Provided a foundation for algebraic computations in categorical contexts
Abstract
In this paper we establish Composition-Diamond lemma for small categories. We give Gr\"obner-Shirshov bases for simplicial category and cyclic category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra