منابع مشابه
Pseudo-commutative Monads
We introduce the notion of pseudo-commutative monad together with that of pseudoclosed 2-category, the leading example being given by the 2-monad on Cat whose 2-category of algebras is the 2-category of small symmetric monoidal categories. We prove that for any pseudo-commutative 2-monad on Cat, its 2-category of algebras is pseudo-closed. We also introduce supplementary definitions and results...
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For a given function f : Σ∗ → Σ∗ over an alphabet Σ, a language X ⊆ Σ∗ is said to f -commute with a language Y ⊆ Σ∗ if the equality XY = f(Y )X holds. This paper investigates the maximal solution to such f -commutative language equations for both morphic and antimorphic involutions f , under the condition that the known quantity (either X or Y ) is a singleton. We prove that, in most cases, the...
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We study approximation of Boolean functions by low-degree polynomials over the ring Z/2kZ. More precisely, given a Boolean function F : {0,1}n {0,1}, define its k-lift to be F : {0,1}n {0,2k-1} by Fk(x) = 2k-F(x) mod 2k$. We consider the fractional agreement (which we refer to as d,k(F)) of Fk(x) with degree d polynomials from Z/2kZ[x1,...,xn]. Our results are the following: 1. Increasing k can...
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We study 2-monads and their algebras using a Cat-enriched version of Quillen model categories, emphasizing the parallels between the homotopical and 2-categorical points of view. Every 2-category with finite limits and colimits has a canonical model structure in which the weak equivalences are the equivalences; we use these to construct more interesting model structures on 2-categories, includi...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2011
ISSN: 0001-8708
DOI: 10.1016/j.aim.2011.06.039