HOCHSCHILD–MITCHELL COHOMOLOGY OF A LOCALLY BOUNDED CATEGORY

Abstract

We consider k-linear categories A which are locally bounded, that is, for every object x, the sums ∑y dim k A(x, y) and ∑y dim k A(y, x) are finite. Let x1,x2,…, be an enumeration of the objects of A such that for each n ∈ ℕ, the full subcategory A(n) of A formed by the objects x1,x2,…,xn is convex in A. We compute the Hochschild–Mitchell cohomology of A as the inverse limit of the cohomologies of the categories A(n).