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The fundamental groupoid scheme and applications

Hélène Esnault, Phùng Hô Hai (2008)

Annales de l’institut Fourier

We define a linear structure on Grothendieck’s arithmetic fundamental group π 1 ( X , x ) of a scheme X defined over a field k of characteristic 0. It allows us to link the existence of sections of the Galois group Gal ( k ¯ / k ) to π 1 ( X , x ) 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...

Traced premonoidal categories

Nick Benton, Martin Hyland (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in cartesian categories.

Traced Premonoidal Categories

Nick Benton, Martin Hyland (2010)

RAIRO - Theoretical Informatics and Applications

Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in Cartesian categories.

Currently displaying 181 – 200 of 206