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 Heyting doctrines
The Hurwitz action and braid group orderings.
The infinite minimal rich monoid
The Khovanov-Lauda 2-category and categorifications of a level two quantum representation.
The low-dimensional homology of crossed modules.
The maximality of the typed lambda calculus and of cartesian closed categories
The monoidal centre as a limit.
The natural number bialgebra
The notion of closedness in topological categories
In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated...
The Obstruction theory of Group Extensions and H^3(Q, A) in Abstract Categories
The separated extensional Chu category.
The stack of microlocal perverse sheaves
In this paper we construct the abelian stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Following ideas of Andronikof we first consider microlocal perverse sheaves at a point using classical tools from microlocal sheaf theory. Then we will use Kashiwara-Schapira’s theory of analytic ind-sheaves to globalize our construction. This presentation allows us to formulate explicitly a global microlocal Riemann-Hilbert correspondence.
The stack quotient of a groupoid
The structure of initial completions
The syntax of coherence
The tensor category of linear maps and Leibniz algebras.
The theory of core algebras: its completeness.
The Whitehead categorical group of derivations.