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It is shown that the endomorphism monoids of the category $2mathfrak{Cob}$ of all $2$-cobordisms do not have finitely axiomatizable equational theories. The same holds for the {topological annular category} and various quotients of the latter, like the affine Temperley--Lieb category. Analogous results are obtained f
We introduce a notion of $n$-commutativity ($0le nle infty$) for cosimplicial monoids in a symmetric monoidal category ${bf V}$, where $n=0$ corresponds to just cosimplicial monoids in ${bf V,}$ while $n=infty$ corresponds to commutative cosimplicial
We give a new syntax independent definition of the notion of a generalized algebraic theory as an initial object in a category of categories with families (cwfs) with extra structure. To this end we define inductively how to build a valid signature $
In this second part of a series work, we further develop the theory of higher fusion categories, including center functors, centralizers and group theoretic higher fusion categories. Along the way we prove several conjectures on modular extensions an
Motivated by recent problems regarding the symmetry of Hecke algebras, we investigate the symmetry of the endomorphism algebra $E_P(M)$ for $P$ a $p$-group and $M$ a $kP$-module with $k$ a field of characteristic $p$. We provide a complete analysis f
It is shown that the category of emph{semi-biproducts} of monoids is equivalent to the category of emph{pseudo-actions}. A semi-biproduct of monoids is a new notion, obtained through generalizing a biproduct of commutative monoids. By dropping commut