# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 2nd 2012

I have finally split off dependent sum from dependent product. And added a few more paragraphs.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 4th 2014

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.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeMar 5th 2017

Is that a little confusing at dependent sum to have it be left adjoint to base change for any $f:A \to I$, then later consider only terminal maps?

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeJun 7th 2018

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 $f: A \to B$, 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?

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeJun 7th 2018

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.