… make use of topological categories, such as the topological category Mfldn of n… a functor
Mfldn → C from a topological category such as Mfldn to an ∞-category C we will always mean a …

… to define the derived category D(A ) of an abelian category A by ‘formally adjoining inverses
… ≫ 0, where H n (P) denotes the n-th homology module of P. If P and Q are such complexes …

… The present paper is devoted to an ezistence proof for a strong homology theory 'h. (theorem
3.1.): Given the categories I(,f as well as a homology theory h, on the subcategory of good …

… In the context of abelian categories, we prove a categorified … by Iyama in the case of module
categories. In this connection we … a homological theory in a general triangulated category T …

… are categories, by we mean the category of functors from A to], and by 'AI we mean the
objects of A. If …

… homology is not) a shape invariant. In the present paper we present a modified shape
category … the usual argument that a homology theory on a category of based spaces leads to a …

… A be the category of pairs of arbitrary topological spaces and continuous mappings and …
on the category Aewill be called a homology theory in the sense of Milnor if it is a homology the…

… a new homology theory for quivers that we call square-commutative homology of quivers,
which is the path homology of a … of a marked category and show that this is a graded algebra …

… The answer to this question is yes - if we accept to expand what we mean by a category.
Indeed, homotopies between maps are something that looks kind of familiar from …

… The reduced homology are natural in the category of pointed topological spaces. Everywhere
… Before de.ning the Steenrod homology we give a brief de-scription of (co)homologies de.…