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We define algebraic structure on a locally finitely presentable W -category for a locally finitely presentable bicategory W with a small set of objects. We further define the W -category of algebras for a given algebraic structure. Each algebraic structure gives rise to a finitary W -monad with...
Given a small pretopos P, we consider the category Mod (P) of models of P indexed over topological spaces. By considering indexed categories of coalgebras, we show that for any indexed functor F: Mod (P) → Mod (Q) , where Q is another small pretopos, the functor F 1 : Mod ( P ) → Mod ( Q )...
We study the Hilbert functions of strongly stable ideals in polynomial rings with restricted powers of the variables.
We give a complete classification up to isomorphisms of complex filiform Lie algebras of dimension m with m ≤ 11.
Homotopy theory for monoid presentations originated by Squier is developed by means of homotopy reduction systems. Two types of asphericity are considered and a relation to the low-dimensional homology is established. If a monoid presentation has a complete homotopy reduction system that is...
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