… Throughout this paper, A will be an exact category satisfying the direct sum axiom. … A is the
category of all A-sheaves, we can define f to be the class of all monomorphisms which yield A…

… In § 3 a homology theory of categories is developed for which the … homology of a category
C can be described briefly s follows. Let AC be the category of Simplexes over the category C …

… A technical difference is that our definitions of homology are, … factorization homology as a
colimit over an ∞-category c D isk … Morrison & Walker define blob homology as a colimit over a …

… the introduction, when C is a small category and R is a commutative ring with a 1 we define
… We may verify that 2-cocycles are homologous if and only if the extensions which produced …

… In this paper we start with a category £, a cotriple G in £, and show how … or homology can
be constructed by means of this tool alone. The category £ will be non-abelian in general (note …

… given examples of homology theories which are not additive. Let W~ denote the category
consisting of all pairs (X, A) such that both X and A have the homotopy type of a CW-complex; …

… A; k.. 0, 1, 2,•••--k _ _ be the corresponding homology functors defined by 1'1. Andr6 in [1].
Let be a category, and G..(I, e., &) a cotriad on(we use the shorter and less ambiguous" triad" …

… a brief review of Lagrangian Floer (co)homology and product structures. Then we introduce
the Fukaya category (informally and without a … wrapped Fukaya categories and outline a few …

… For the expert we note a few special features. The basic functors Ext and Tor are described
… a category to be a class of objects.... We call a category small if the class of its objects is a …

… functors of colimit define a homology theory for Rat, the category of small categories. In
this paper, we show that, up to natural isomorphism, there is only one such homology theory. …