iX:X→X∐Y is the inclusion map.
what makes a coproduct an “inclusion mapping”? I haven’t seen this convention/synonym anywhere before.
“inclusion map” refers to the map iX, not the coproduct X∐Y. The map iX is a coprojection (these are sometimes called “inclusions”, see https://ncatlab.org/nlab/show/coproduct).
A simple example in sets: We have two sets X, Y, and their disjoint union X⊔Y. Then the inclusion map iX is the map that maps x (as an element of X) to x (as an element of X⊔Y).
what makes a coproduct an “inclusion mapping”? I haven’t seen this convention/synonym anywhere before.
“inclusion map” refers to the map iX, not the coproduct X∐Y. The map iX is a coprojection (these are sometimes called “inclusions”, see https://ncatlab.org/nlab/show/coproduct).
A simple example in sets: We have two sets X, Y, and their disjoint union X⊔Y. Then the inclusion map iX is the map that maps x (as an element of X) to x (as an element of X⊔Y).