We show that stable derivators, like stable model categories, admit Mayer-Vietoris sequences arising from cocartesian squares. Along the way we characterize homotopy exact squares, and give a detection result for colimiting diagrams in derivators. As an application, we show that a derivator is stable if and only if its suspension functor is an equivalence.

By studying certain kind of centralizer algebras of the affine Schur algebra S̃(n, r) we show that S̃(n, r) is Noetherian and we determine its center. Assuming n ≥ r, we show that S̃(n+ 1, r) is Morita equivalent to S̃(n, r), and the Schur functor is an equivalence under certain conditions.

In this note we present a combinatorial link invariant that underlies some recent stable homotopy refinements of Khovanov homology of links. The invariant takes the form of a functor between two combinatorial 2-categories, modulo a notion of stable equivalence. We also develop some general properties of such functors.

Let Fp denote the field with p elements and F̄p its algebraic closure. We show that the singular cochain functor with coefficients in F̄p induces a contravariant equivalence between the homotopy category of connected pcomplete nilpotent spaces of finite p-type and a full subcategory of the homotopy category of E∞ F̄p-algebras. Draft: January 26, 1998, 17:28

Abramsky’s domain equation for bisimulation and the author’s categorical models for names combine to give a domain-theoretic model for the π-calculus. This is set in a functor category which provides a syntax-free interpretation of fresh names, privacy, visibility and non-interference between processes. The model is fully abstract for strong late bisimilarity and equivalence (bisimilarity under...

We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.

The assignment (nonstable K0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (i) There is no functor Γ, from simplicial monoids with order-unit with normalized positive homomorphisms t...

We show that each of the three K-theory multifunctors from small permutative categories to $$\mathcal {G}_*$$ -categories, -simplicial sets, and connective spectra, is an equivalence homotopy theories. For these multifunctors, we describe explicit inverse functor. As a separate application our general results about pointed diagram categories, observe right-induced theory Bohmann–Osorno {E}_*$$ ...

Let $${\mathcal {C}}$$ be an n-angulated category. We prove that its idempotent completion $$\widetilde{{\mathcal {C}}}$$ admits a unique structure such the canonical functor $$\iota : {\mathcal {C}}\rightarrow \widetilde{{\mathcal is n-angulated. Moreover, $$ induces equivalence $$Hom _{n-ang }(\widetilde{{\mathcal {C}}},{\mathcal {D}})\cong Hom }({\mathcal {C}},{\mathcal {D}})$$ for any c...

Let Sp denote the category of spaces, Ho the associated homotopy category, and D a small (index) category. A diagram in Ho with the shape of D is by definition a functor F : D −→ Ho. Given such a diagram one can ask whether or not it has a realization, i.e., a lift to a functor D −→ Sp, and if so, how many realizations there are up to an appropriate kind of equivalence. This question is studied...