Re: "injective" terminology

I always thought that ind-object in the work of Grothendieck and the SGA seminars was short for inductive object. Tim On 21/05/2010 18:35, Toby Bartels wrote:

The term "projective limit" contrasts with "inductive limit", so I have sometimes felt like saying "inductive object".

However, I've never actually done so; besides having no precedent, the term "inductive object" already has an established meaning: an inductive object is an initial algebra of a polynomial endofunctor. (Example: A natural-numbers object is an initial algebra of X + 1. The dual to this concept is unimaginatively called "coinductive".) This is used in logic and computer science.

--Toby

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