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Created Gamma-space.
Hi there Matan. Editing is easy! Open the page, go to Edit. (and if you want to add a reference see if that reference is somewhere else in the lab! That makes life easy if it .. copy from the source of that page into where you want the reference to go.)
have a look at the source and … do the obvious things. If it goes wrong go back to the previous version and call for help!!!!!
(Some seconds later: I was going to give you a hand but note that you are actually editing that page anyway….. )
One point to add would be to make the names point to the relevant page entries, also any pages you know exist can be linked so G. Segal should work but did not (but I did a redirect).
I see you solved the mystery!!! My methods are either to put in the link in an existing (relevant) entry, or to search on the term and if it does not exist and is useful, the search page suggests that you create it.
It is always better to search first (and with possible alternative titles) as that we we don’t get too many needs to merge entries. Clearly someone else may have used a slightly different term for something or it may be hidden in another entry. If a mention is hidden in another entry it is a good thing to go in to that and convert the term to a link.
I wonder if jim is meaning Theta-space? They certainly look to be related but am not up on those as much as I should be.
It would be good if you added a bit more about your research interests on your own page.
The introduction seems to be misleading: a grouplike $\Gamma$-space is an infinite loop space, but are $\Gamma$-spaces automatically grouplike? It appears to me, for instance, that any commutative monoid gives rise to a $\Gamma$-space.
Thanks for the alert, I have fixed the wording.
Added:
One of the main advantages of $\Gamma$-spaces (and, more generally, $\Gamma$-objects) is that the delooping construction is very easy to express in this language.
The delooping construction is a functor
$B\colon Fun(\Gamma^{op},M) \to Fun(\Gamma^{op},M),$where $M$ is the relative category for which we are considering $\Gamma$-objects. The most common choices are $M=sSet$, the model category of simplicial sets, and $M=Top$, the model category of topological spaces.
We define
$(B A)(S) := hocolim (T\mapsto A(S\times T)),$where $T\in\Delta^\op$ and the argument of the homotopy colimit functor is a simplicial object in $M$. Here $T\in\Delta$ is converted first to an object of $\Gamma$ via the functor $\Delta\to\Gamma$ described below.
Added:
Another early reference considers $\Gamma$-objects in simplicial groups. It is also the first reference that uses the terms “special Γ-spaces” and “very special Γ-spaces”, which it attributes to Segal.
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