In the efforts to define a 2-categorical analog of an abelian category, two (or three) notions of “abelian 2-categories” are defined in [4] and [2]. One is the relatively exact 2-category defined in [4], and the other(s) is the (2-)abelian Gpd-category defined by Dupont [2]. We compare these notions, using the arguments in [4] and [2]. Since they proceed independently in their own way, in diffe...

A function complex is introduced on the category of flows so that the model category of flows becomes a simplicial model category. This allows us to show that the homotopy branching space of the cone of a morphism of flows is homotopy equivalent to the cone of its image by the homotopy branching space functor. The crux of the proof is that the homotopy branching space of the terminal flow is co...

Let G = SpecA be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗ = R × B∗ as R-algebras and the first projection A∗ → R is the unit of A. If M is a dual functor of G-modules and wG := (1, 0) ∈ R×B ∗ =...

Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups SCG are being investigated. In this paper, we consider a 2-categorical analogue of an abelian category, in such a way that it contains SCG as an example. As a main theorem, we ...

We exhibit a surprising connection between the following two concepts: Brown representability which arises in stable homotopy theory, and flat covers which arise in module theory. It is shown that Brown representability holds for a compactly generated triangulated category if and only if for every additive functor from the category of compact objects into the category of abelian groups a flat c...

For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are characterized and two consequences for the class of hereditary rings are established: homological epimorphisms and universal localizations coincide, and the tel...

Let X be a compact real analytic manifold, and let T ∗X be its cotangent bundle. Let Sh(X) be the triangulated dg category of bounded, constructible complexes of sheaves on X. In this paper, we develop a Fukaya A∞-category Fuk(T ∗X) whose objects are exact, not necessarily compact Lagrangian branes in the cotangent bundle. We write TwFuk(T ∗X) for the A∞-triangulated envelope of Fuk(T ∗X) consi...

The Halstead Category Test of brain dysfunction is one of the most sensitive neuropsychological measures currently available. While the instrument has received widespread use, nevertheless, the exact nature of what it measures has been poorly delineated. The present brief report presents the results of separate factor analyses of the Category Test along with other neuropsychological measures fr...

Background/Aims Although high-resolution manometry (HRM) has the advantage of visual intuitiveness, its diagnostic validity remains under debate. The aim of this study was to evaluate the diagnostic accuracy of HRM for esophageal motility disorders. Methods Six staff members and 8 trainees were recruited for the study. In total, 40 patients enrolled in manometry studies at 3 institutes were s...