Associativity and the cosmash product in operadic varieties of algebras

DOI10.1215/00192082-10678862zbMath1529.18018arXiv2206.12096OpenAlexW4386248776MaRDI QIDQ6183825

Tim Van der Linden, Corentin Vienne, Ülo Reimaa

Publication date: 4 January 2024

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.12096

zbMATH Keywords

commutatorscosmash productsoperadic variety of algebras

Mathematics Subject Classification ID

Equational categories (18C05) Automorphisms and endomorphisms of algebraic structures (08A35) Categories of algebras (08C05) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Algebraic operads, cooperads, and Koszul duality (18M70) Protomodular categories, semi-abelian categories, Mal'tsev categories (18E13)

Cites Work

• Normalities and commutators
• Quadratic functors on pointed categories
• Central reflections and nilpotency in exact Mal'tsev categories
• Smash product of pointed objects in lextensive categories
• A characterisation of Lie algebras via algebraic exponentiation
• Algebraic exponentiation in general categories
• The ternary commutator obstruction for internal crossed modules
• A characterisation of Lie algebras amongst anti-commutative algebras
• Varieties of algebras
• Internal object actions in homological categories
• Encyclopedia of Types of Algebras 2010
• Groups with Multiple Operators
• Algebraically coherent categories
• Algebras with representable representations
• Categorical algebra
• Non-associative Algebras
• Algebraic Operads
• Semi-abelian categories
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