Abstract
Let E=(A,S) be an exact category with enough projectives P. We introduce the notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of support τ-tilting modules (subcategories) in various contexts. It is also a generalization of tilting subcategories of exact categories. We show that there is a bijection between support τ-tilting subcategories and certain τ-cotorsion pairs. Given a support τ-tilting subcategory T, we find a subcategory ET of E which is an exact category and T is a tilting subcategory of ET. If E is Krull-Schmidt, we prove the cardinal |T| is equal to the number of isomorphism classes of indecomposable projectives Q such that HomE(Q,T)≠0. We also show a functorial version of Brenner-Butler's theorem.
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