-catégories (catégories dans un triple)
Tenseurs et machines
Tensor-triangulated categories and dualities.
TFT Construction of RCFT correlators. V: Proof of modular invariance and factorisation.
The affineness criterion for quantum Hom-Yetter-Drinfel'd modules
Quantum integrals associated to quantum Hom-Yetter-Drinfel’d modules are defined, and the affineness criterion for quantum Hom-Yetter-Drinfel’d modules is proved in the following form. Let (H,α) be a monoidal Hom-Hopf algebra, (A,β) an (H,α)-Hom-bicomodule algebra and . Under the assumption that there exists a total quantum integral γ: H → Hom(H,A) and the canonical map , , is surjective, we prove that the induction functor is an equivalence of categories.
The algebraic groups leading to the Roth inequalities
We determine the algebraic groups which have a close relation to the Roth inequalities.
The Brauer and Brauer-Taylor groups of a symmetric monoidal category
The category of disintegration
The catgorical theory of self-similarity.
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput. 37 (2007) 977–1013].
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].
The Frobenius relations meet linear distributivity.
The fundamental groupoid scheme and applications
We define a linear structure on Grothendieck’s arithmetic fundamental group of a scheme defined over a field of characteristic 0. It allows us to link the existence of sections of the Galois group to with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering of the affine...
The Hurwitz action and braid group orderings.
The infinite minimal rich monoid
The monoidal centre as a limit.
The tensor category of linear maps and Leibniz algebras.
The Whitehead categorical group of derivations.
Théorie de Schreier supérieure
Third Mac Lane cohomology via categorical rings.