Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I have finally split off dependent sum from dependent product. And added a few more paragraphs.
Added a section Relation to some limits with the remarks that dependent sum to the points preserves fiber products and that the naturality squares of the unit are pullbacks.
Is that a little confusing at dependent sum to have it be left adjoint to base change for any , then later consider only terminal maps?
Returning to my comment in #3, do type theorists use the terms dependent sum (or pair) and dependent product for adjoints to base change for general , or only for terminal maps?
Does anyone know the history of this? When did Martin-Löf first talk about dependent sum/product? Would he use the terms in the more general sense?
I don’t know the history. In general, dependent sum/product are used in type theory for syntax that corresponds to adjoints to base change along a display map (i.e. to a map with terminal codomain, but in an arbitrary context). But since every map is isomorphic (in extensional type theory) or equivalent (in homotopy type theory) to a display map, in category theory we tend to use the words for adjoints to base change along an arbitrary map.
1 to 6 of 6