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Operads of decorated trees and their duals

Vsevolod Yu. Gubarev, Pavel S. Kolesnikov (2014)

Commentationes Mathematicae Universitatis Carolinae

This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform...

Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles.

Christian Léger (1991)

Revista Matemática de la Universidad Complutense de Madrid

We call metamorphosis of a given category an autoequivalence functor up to within natural equivalence. We show that, given a group G, the group of metamorphoses of the category of G-sets (as well as the corresponding group for ?sufficiently big? subcategories) may be naturally identified to the group of outer automorphism of G. We get by this way a natural description of a group of known operations on tessellations of a surface: the identity operation, the Poincaré duality, and four others which...

Opmonoidal monads.

McCrudden, Paddy (2002)

Theory and Applications of Categories [electronic only]

Order-enriched solid functors

Lurdes Sousa, Walter Tholen (2019)

Commentationes Mathematicae Universitatis Carolinae

Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnková's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by C. Anghel. Our focus in this paper is on differentiating...

Ordinary differential equations and their exponentials

Anders Kock, Gonzalo Reyes (2006)

Open Mathematics

In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.

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