The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces based topological spaces. We construct between complexification-realification adjunction These allow for movement versions calculi, comparisons Taylor towers produced by both calculi. show that when inputted functor is weakly polynomial, tower restricted through realifica...

We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (= interior tensor product) with a strong Morita equivalence bimodule. Date: Septembe...

For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...

In this paper we present background results in enriched category theory and model necessary for developing categories of functors suitable doing functor calculus.

For simplicity we adopt the following convention: I, X denote sets, M denotes a many sorted set indexed by I, R1 denotes a binary relation on X, and E1, E2, E3 denote equivalence relations of X. We now state the proposition (1) (E1 ⊔ E2) ⊔ E3 = E1 ⊔ (E2 ⊔ E3). Let X be a set and let R be a binary relation on X. The functor EqCl(R) yielding an equivalence relation of X is defined as follows: (De...

Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (F-coalgebras) and a notion of behavioral equivalence (∼F) amongst them. Many types of transition systems and their equivalences can be captured by a functor F. For example, for deterministic automata the derived equivalence is language equivalen...

In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and triangulated category of singularities of the fiber of W over zero. We also proved that the category of graded D-branes of type B in such LG-models is connected by a fully faithful functor with the derived category of coherent sheaves on the...

We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simply algebras which are projective in the variety they generate. A byproduct of our efforts is the result that if A and B are strictly simple and generate the same variety, then A$B ...

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of com...

Let I be a small indexing category, G : I → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicial sets (resp. categories) indexed on BG and the category of I-diagrams over N(G) (resp. G). As an application we obtain a Quillen equivalence between the categories of presheaves of simplicial sets (re...