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Categorical methods in graded ring theory.

Angel del Río (1992)

Publicacions Matemàtiques

Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.

Categorical Pullbacks

Marco Riccardi (2015)

Formalized Mathematics

The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown there that ordinal numbers can be considered as categories. Then the pullback is introduced in terms of its universal property and the Pullback Lemma is formalized [15]. In the last part of the article we formalize the pullback of functors [14] and it...

Catégorie homotopique stable d’un site suspendu avec intervalle

Joël Riou (2007)

Bulletin de la Société Mathématique de France

Cet article présente la construction de la catégorie homotopique stable d’un site suspendu avec intervalle arbitraire. La fonctorialité de cette construction est étudiée, avec des applications à la théorie homotopique des schémas introduite par F. Morel et V. Voevodsky.

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