Here HOM is the functor category, π∗ is induced by the natural projection π : hocolimI C −→ I, 0 is the category with only one map and id maps the only object of 0 to the identity functor. A reason for using the above definitions is that taking nerves one recovers the usual homotopy (co)limits for simplicial sets, up to homotopy in the case of hocolim ([T]) and up to isomorphism in the case of ...

The aim of the paper is to work towards a generalisation of coalgebraic logic enriched over a commutative quantale. Previous work has shown how to dualise the coalgebra type functor T : Ω-Cat //Ω-Cat in order to obtain the modal operators and axioms describing transitions of type T . Here we give a logical description of the dual of Ω-Cat.

We show that Rieffel’s functor sends covariant C(T )-algebras in C(T )-algebras and covariant continuous fields of C∗-algebras in continuous fields of C∗-algebras. We use this to prove spectral continuity results for families of Rieffel-type pseudodifferential operators.

Let T be a triangulated category with coproducts, T ⊂ T the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [1]: All homological functors {T} −→ Ab are the restrictions of representable functors on T, and all natural transformations are the restrictions of morphisms in T. It has been something of a mystery, to what extent this ge...

Consider a commutative ring $R$ and simplicial map, $X\mathop {\longrightarrow }\limits ^{\pi }K,$ of finite complexes. The cochain complex $X$ with coefficients, $\Delta ^*X,$ then has the structure an $(R,K)$ chain complex, in sense Ranicki . Therefore it Ranicki-dual $T \Delta ^*X$ This (contravariant) duality functor $T:\mathcal {B} R_K\to \mathcal R_K$ was defined algebraically on category...

Abstract We introduce a new approach to the study of finite-dimensional representations quantum group affine Lie superalgebra $ \textrm {L}{\mathfrak {g}\mathfrak {l}}_{M|N}=\mathbb {C}[t,t^{-1}]\otimes \mathfrak {l}_{M|N}$ ($M\neq N$). explain how {l}}_{M|N}$ are directly related those algebra type $A$, using an exact monoidal functor called truncation. This can be viewed as analogue super dua...

Let T be a triangulated category with coproducts, T ⊂ T the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [1]: All homological functors {T}op −→ Ab are the restrictions of representable functors on T, and all natural transformations are the restrictions of morphisms in T. It has been something of a mystery, to what extent this ...

2 A bimodule realization of the Temperley-Lieb two-category 8 2.1 Ring A and two-dimensional cobordisms . . . . . . . . . . . . 8 2.2 Flat tangles and the Temperley-Lieb category . . . . . . . . . 10 2.3 The Temperley-Lieb 2-category . . . . . . . . . . . . . . . . . 12 2.4 The ring H . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5 Projective H-modules . . . . . . . . . . . . . . ....

For each recollement of triangulated categories, there is an epivalence between the middle category and comma associated with a triangle functor from on right to left. morphic enhancement $\mathcal {T}$ , are three explicit ideals enhancing category, whose corresponding factor categories all equivalent module over . Examples related inflation weighted projective lines discussed.