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Coproducts of ideal monads

Neil Ghani, Tarmo Uustalu (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...

Coproducts of Ideal Monads

Neil Ghani, Tarmo Uustalu (2010)

RAIRO - Theoretical Informatics and Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly  [Bull.  Austral. Math. Soc.22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell.2309 (2002)...

Definable orthogonality classes in accessible categories are small

Joan Bagaria, Carles Casacuberta, A. R. D. Mathias, Jiří Rosický (2015)

Journal of the European Mathematical Society

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka’s principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy. For example, the statement that, for a class 𝒮 of morphisms in a locally presentable category 𝒞 of structures, the orthogonal class of objects is a small-orthogonality...

Descent for monads.

Hofstra, Pieter, De Marchi, Federico (2006)

Theory and Applications of Categories [electronic only]

Distributive laws and Koszulness

Martin Markl (1996)

Annales de l'institut Fourier

Distributive law is a way to compose two algebraic structures, say 𝒰 and 𝒱 , into a more complex algebraic structure 𝒲 . The aim of this paper is to understand distributive laws in terms of operads. The central result says that if the operads corresponding respectively to 𝒰 and 𝒱 are Koszul, then the operad corresponding to 𝒲 is Koszul as well. An application to the cohomology of configuration spaces is given.

Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras

Michael M. Zarichnyi (1991)

Commentationes Mathematicae Universitatis Carolinae

We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.

Currently displaying 101 – 120 of 380