1 Essential data

Let us consider an abelian category 𝒞 which is locally small and a dense subcategory 𝒜 of 𝒞, with T : 𝒞→𝒞∕𝒜 being the canonical functor. Moreover, let us assume that T has a right adjoint denoted by S such that one has the following functorial isomorphism, or natural equivalence:

.

Definition 1.1. The right adjoint functor

of T– which is specified by the essential data above– is called a section functor.

Note: the category 𝒜 is defined as a localizing subcategory.

Reference cited.