Functoriality

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title: Functoriality permalink: wiki/Functoriality/ layout: wiki

Friday

Discussions started -- a package Functoriality will be created from Jason and Chris' pre-existing work, to make Hom, Tor, and Ext properly functorial [and possibly implement some change-of-rings code?]. This is to be put together on Saturday morning.

DerivedCategory might get created -- we'll talk to Dan on Saturday to see what this would entail.

SpectralSequences -- we had some questions about memory for Mike but it looks like this is a possible way to go. More on Saturday.

This group split off for Friday afternoon into other groups, some working on Power Series Rings and some on old projects.

Saturday

Functoriality has some work done on it now -- the two implementations of connectingHomomorphism are getting worked out. Ext and Tor should now both be able to take maps. Things to do:

• connectingTor and connectingExt optimization is necessary for doing only one piece of the connecting map. [Chris+Jason for math: how much of the chain complexes P**L, P**M, and P**N are really needed to find the second piece of the Tor connecting map?, Chris for code]
• coneInjectTarget et al need to be worked into the connectingHomomorphism code [Chris]
• coneInjectTarget et al need documentation. [Jason]
• @TO in the documentation. [Chris]
• Needs TEST assertions. [Jason]
• change of rings functions maybe. [Jason]

ExtFunctor is getting completed finally, one of Chris' ongoing projects.

Sunday

These people spent all of Sunday on Power Series.

Tuesday

Documentation day. Jason: document the 4 cone functions and the 2 Tors Chris' connecting homomorphism is implemented for now, but note that Jason's connecting homomorphism code is twice as fast and 90% as correct, but only 25% as finished so it is not included. Chris: horseshoe documentation issue

Thursday 8/12/2010

Work on the Functoriality package has been revived. After discussions with Dan Grayson and Mike Stillman, we are making Tor and Ext properly functorial, with an optional "Prune" argument. This argument will default to 'false' so that Tor_0(M,N) and M ** N will be equal and Ext^0(M,N) and Hom(M,N) will be as well. This code will either go in the Functoriality package or just directly into the core code. Here are the methods already implemented:

Tor(ZZ,Module,Module)

Tor(ZZ,Matrix,Module)

Tor(ZZ,Module,Matrix)

Ext(ZZ,Module,Module)

Ext(ZZ,Matrix,Module)

Ext(ZZ,Module,Matrix)

Methods yet to be implemented/updated:

connectingTor

connectingExt

Other finished methods:

toHom

horseshoe

Also maybe:

Change of rings type methods for Hom,tensor,Tor,Ext

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