10 citations · 20 across the 11 of their papers we have counts for
14 papers
On the (algebraic) notion of 2-ring
Josep Elgueta
By a 2-ring we mean a groupoid with a structure analogous to that of a ring, up to coherent isomorphisms. Two different notions of 2-ring appear in the literature: the notion of {\…
An alternative description of symmetric monoidal categories, and symmetric 2-groups
Josep Elgueta
An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms,…
Normal submonoids and congruences on a monoid
Josep Elgueta
A notion of {\em normal submonoid} of a monoid is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set of normal…
The groupoid of finite sets is biinitial in the 2-category of rig categories
Josep Elgueta
The groupoid of finite sets has a "canonical" structure of a symmetric 2-rig with the sum and product respectively given by the coproduct and product of sets. This 2-rig $\widehat{…
Endomorphisms of the symmetric 2-rig of finite sets
Josep Elgueta
Let be the groupoid of finite sets and bijections between them equipped with the canonical symmetric rig category structure given by the disjoint…
On the representations of 2-groups in {Baez-Crans} 2-vector spaces
Benjamín Alarcón Heredia, Josep Elgueta
We prove that the theory of representations of a finite 2-group in Baez-Crans 2-vector spaces over a field of characteristic zero essentially reduces to the theory…
Permutation 2-groups I: structure and splitness
Josep Elgueta
By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a one-object…
The 2-group of symmetries of a split chain complex
Josep Elgueta
We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any {\it split} chain complex in an arbitrary $\kb$…
On the regular representation of an (essentially) finite 2-group
Josep Elgueta
The regular representation of an essentially finite 2-group in the 2-category of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology…
Generalized 2-vector spaces and general linear 2-groups
Josep Elgueta
In this paper a notion of {\it generalized 2-vector space} is introduced which includes Kapranov and Voevodsky 2-vector spaces. Various kinds of generalized 2-vector spaces are con…
Representation theory of 2-groups on finite dimensional 2-vector spaces
Josep Elgueta
In this paper, the 2-category of (weak) representations of an arbitrary (weak) 2-group on (some version of) Kapr…
A strict totally coordinatized version of Kapranov and Voevodsky's 2-category {\bf 2Vect}
Josep Elgueta
We give a concrete description of a strict totally coordinatized version of Kapranov and Voevodsky's 2-category of finite dimensional 2-vector spaces. In particular, we give explic…
2-cosemisimplicial objects in a 2-category, permutohedra and deformations of pseudofunctors
Josep Elgueta
In this paper we take up again the deformation theory for -linear pseudofunctors initiated in a previous work (Adv. Math. 182 (2004) 204-277). We start by introducing a notion o…
Cohomology and deformation theory of monoidal 2-categories I
Josep Elgueta
We define a cohomology for an arbitrary -linear semistrict semigroupal 2-category (called in the paper a Gray semigroup) and show that its first order (…