Dear All,

I hope all is well.

Upon [re]reading Professor F. William Lawvere's discussion of Grothendieck's definition of subobject:

"It became clear in the early sixties that the definition of SUBOBJECT given by Grothendieck is not a pretense, circumlocution, or paraphrase, but the only correct definition.  Here 'correct' means in a foundational sense, i.e. the only definition universally and compatibly applicable across all the branches of mathematics:

a subobject is NOT an object, but a given inclusion map.

The intersection of two objects has no sense, for only maps (with common codomain) can overlap" ( https://github.com/punkdit/categories/blob/master/www.mta.ca/cat-dist/archive/1996/96-3 lines 2756-; also attached, pp. 4-5).

I am very much enthusiastic about studying the original paper / book, where Grothendieck redefined subobject.  I'd be truly grateful to you for your insights into the context (problem / theory) that motivated Grothendieck's redefinition of subobject.

Thanking you,

Yours truly,

posina