Tootfinder

Compatibility between truncation and coproducts for quantum affine algebra and Yangian of $\mathfrak{sl}_2(\mathbb{C})$
J\'er\^ome Milot
https://arxiv.org/abs/2506.10544

Compatibility between truncation and coproducts for quantum affine algebra and Yangian of $\mathfrak{sl}_2(\mathbb{C})$
We prove that the standard Drinfeld-Jimbo coproducts for Yangians and quantum affine algebras factorize through their truncated quotients in the case of $\mathfrak{sl}_2(\mathbb{C})$.

This https://arxiv.org/abs/2405.19258 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Polyhedral coproducts
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral coproducts, surveying the Eckmann-Hilton duals of various familiar examples and properties of polyhedral products. In particular, we show that polyhedral coproducts give a functorial interpolation between the wedge and cartesian product of spaces which differs from the…

A categorical formulation of the Deligne-Terasoma approach to double shuffle theory
Benjamin Enriquez, Khalef Yaddaden
https://arxiv.org/abs/2506.15348 htt…

A categorical formulation of the Deligne-Terasoma approach to double shuffle theory
In this paper, we introduce the notion of a bimodule with a factorization structure (BFS) and show that such a structure gives rise to an algebra morphism. We then prove that this framework offers an interpretation of the geometric construction underlying both the Betti and de Rham harmonic coproducts of the double shuffle theory developed in \cite{DeT, EF1, EF2, EF3}.

The algebraic small object argument as a saturation
Evan Cavallo, Christian Sattler
https://arxiv.org/abs/2506.02759 https://arxiv.or…

The algebraic small object argument as a saturation
We analyze the structure of left maps in algebraic weak factorization systems constructed using Garner's algebraic small object argument. We find that any left map can be constructed from generators in Bourke and Garner's double category of left maps by operations that parallel the classical cell-complex-forming operations of Quillen's small object argument (coproducts, cobase changes, transfinite composites, and retracts). Our main theorems are phrased as "saturation" principles, which express…