On functors between categories of modules over trusses

On Gr-functors between Gr-categories

Each Gr-category (or categorical group) is Gr-equivalent to a Grcategory of type (Π, A, ξ), where Π is a group, A is a Π-module and ξ is a 3-cocycle of Π, with coefficients in A. In this paper, first we show that each Gr-functor induces one between Gr-categories of type (Π, C). Then we give results on the existence of Gr-functor and the classification of Gr-functors by cohomology groups H(Π, C)...

Benoit Fresse Modules over Operads and Functors

Right Modules over Operads and Functors

In the theory of operads we consider generalized symmetric power functors defined by sums of coinvariant modules. One observes classically that the symmetric functor construction provides an isomorphism from the category of symmetric modules to a split subcategory of the category of functors on dgmodules (if dg-modules form our ground category). The purpose of this article is to obtain a simila...

Functors between Reedy Model Categories of Diagrams

If D is a Reedy category and M is a model category, the category M of D-diagrams in M is a model category under the Reedy model category structure. If C → D is a Reedy functor between Reedy categories, then there is an induced functor of diagram categories M → M. Our main result is a characterization of the Reedy functors C → D that induce right or left Quillen functors M → M for every model ca...

On Closed Categories of Functors

Brian Day Received November 7, 19~9 The purpose of the present paper is to develop in further detail the remarks, concerning the relationship of Kan functor extensions to closed structures on functor categories, made in "Enriched functor categories" | 1] §9. It is assumed that the reader is familiar with the basic results of closed category theory, including the representation theorem. Apart fr...