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.
