[-- Attachment #1.1: Type: text/plain, Size: 1287 bytes --] Question regarding terminology regarding injectivity of objects: (1) An object D is called injective over an arrow j:X->Y if the "restriction map" hom(Y,D) -> hom(X,D) g |-> g o j is a surjection. This is fairly standard terminology (where does it come from, by the way). (2) I am working with the situation where the restriction map is a **split** surjection. I thought of the terminology "D is split injective over j", but perhaps this is awkward. Is there a standard terminology for this notion. Or, failing that, a terminology that at least one person has already used in the literature or in the folklore. Or, failing that too, a good suggestion by any of you? (Before anybody says that there is no difference assuming choice, I remark that I am interested in the "infty-category of types (in a universe)" in HoTT/UF, where the homs are infty-groupoids and so the section has to be a morphism, not just a theoretical function.) Thanks, Martin -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. [-- Attachment #1.2: Type: text/html, Size: 1715 bytes --]