On finiteness spaces and extensional presheaves over the Lawvere theory of polynomials

Thomas Ehrhard (1)

1 PPS - Preuves, Programmes et Systèmes

We define a faithful functor from a cartesian closed category of linearly topologized vector spaces over a field and generalized polynomial functions to the category of ``extensional'' presheaves over the Lawvere theory of polynomial functions, and show that, under some conditions on the field, this functor is full and preserves the cartesian closed structure.

Mots clés: linearly topologized vector spaces; presheaves; linear logic; polynomials

Domaines: Logique en informatique [cs.LO]

Thomas Ehrhard. On finiteness spaces and extensional presheaves over the Lawvere theory of polynomials. 2007. ⟨hal-00165230⟩