The existence and construction of Lax limits
The Exponential Law of Maps. II.
The extensive completion of a distributive category.
The Extraordinary Derived Category.
The first k-invariant, Quillen's space BG+ and the construction of Kann and Thurston.
The five- and nine-lemmas in P-semi-abelian categories.
The Formal Dimension of a Toplogical Space.
The frame of fibrewise closed nuclei
The free adjunction
The Frobenius relations meet linear distributivity.
The functor for the ring of integers of a number field
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 Galois-module structure of the space of holomorphic differentials of a curve.
The genesis of mathematical structures, as exemplified in the work of Charles Ehresmann
The Geometry of Self-adjunction
The Gersten conjecture for Witt groups in the equicharacteristic case.
The Grothendieck group of GL(F)×GL(G)-equivariant modules over the coordinate ring of determinantal varieties
The Hermitian Morita theorems.
The Heyting doctrines
The Hochschild cohomology ring of the singular cochain algebra of a space
We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra....