1 Belian categories 3 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Diagram chase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Snake Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Delta functors . . . . . . . . . . . . . . . . . . . . ....

1 Belian categories 3 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Diagram chase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Snake Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Delta functors . . . . . . . . . . . . . . . . . . . . ....

For a differential graded k-quiver Q we define the free A∞-category FQ generated by Q. The main result is that the restriction A∞-functor A∞(FQ,A) → A1(Q,A) is an equivalence, where objects of the last A∞-category are morphisms of differential graded k-quivers Q → A. A∞-categories defined by Fukaya [Fuk93] and Kontsevich [Kon95] are generalizations of differential graded categories for which th...

Watts’s Theorem says that a right exact functor F : ModR → ModS that commutes with direct sums is isomorphic to − ⊗R B where B is the R-S-bimodule FR. The main result in this paper is the following: if A is a cocomplete category and F : ModR→ A is a right exact functor commuting with direct sums, then F is isomorphic to − ⊗R F where F is a suitable R-module in A, i.e., a pair (F , ρ) consisting...

We introduce a precise notion, in terms of few Schlessinger's type conditions, of extended deformation functors which is compatible with most of recent ideas in the Derived Deformation Theory (DDT) program and with geometric examples. With this notion we develop the (extended) analogue of Schlessinger and obstruction theories. The inverse mapping theorem holds for natural transformations of ext...

We study homological algebra in the abelian category Γ̃, whose objects are functors from finite pointed sets to vector spaces over Fp. The full calculation of Tor ∗ -groups between functors of degree not exceeding p is presented. We compare our calculations with known results on homology of symmetric groups, Steenrod algebra and functor homology computations in the abelian category F of functors...

Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions, conjunction, disjunction, box and diamond. In this paper, we provide a coalgebraic analysis of this theorem...

We investigate how finitary functors on Set can be extended or lifted to finitary functors on Preord and Poset and discuss applications to coalgebra.

Standard ML has a module system that allows one to deene para-metric modules, called functors. Functors are \\rst-order," meaning that func-tors themselves cannot be passed as parameters or returned as results of functor applications. This paper presents a semantics for a higher-order module system which generalizes the module system of Standard ML. The higher-order functors described here are ...