... computability models suit best. It is strict computability models that are constructed here in a canonical way over categories and presheaves on them ² . We structure this paper as follows. In Section 2 , we introduce the notion of a strict computability model over a (possibly proper) class...

...This chapter begins by posing the question of linguistic meaning within the context of the mathematics of category theory. It then explains the notions of functor categories, natural transformations and presheaves. A formal theory of diagrammatic signs building on Peirce’s semiotic theory...

...) holds then BL(n − 1) holds and that H90(n) implies H90(n − 1). Next, the chapter turns to the cohomology of singular varieties, cohomology with supports, and rationally contractible presheaves. From there, it argues that Bloch–Kato implies Beilinson–Lichtenbaum and concludes the theorems by proving...

... π(b)) b ⊩ φ · f This chapter introduces new kinds of models for constructive set theories based on categories of presheaves. It concentrates on categories of classes rather than sets, following the lines of algebraic set theory. It defines...

...This chapter provides the ¹-local projective model structure on the categories of simplicial presheaves and simplicial presheaves with transfers. These model categories, written as Δ^opPshv( Sm ) ₁ and Δ^op PST ( Sm ) ₁, are first defined...