Back to Sydney
I proposed, and ANU accepted, that I change to external student status in order to pester the category theorists in Sydney for another year. Thanks to the running, cycling and training around of anya_1984, I now have a deposit on what seems to be a nice 2 bedroom apartment in the inner west - I'll check it out and (hopefully) sign the lease on my return to Sydney.
I'll be back in Canberra around Sept 16 to go to a concert with elfishski and (probably) give at least one talk on my current research. On the flip side, Canberrans (or other non-Sydneysiders) who want to come up to Sydney to see a concert or such, will soon have a sleeper couch on which to rest their tired heads.
The week after that is the AustMS conference, conveniently located this year at Macquarie. This will be my third year in a row going to this conference - it's fast becoming one of the events I look forward to each year. Anyone else going?
I have also started trying to learn Russian. anya_1984 eventually managed to convince me that there is a difference in the way you pronounce ш and щ. I think that I can even vaguely pronounce them correctly. I guess this is a start at least...
I'll be speaking in the category theory special session. I'll probably be hanging out there and in the combinatorics and group theory special sessions for the most part.
Title: Associative categories
Abstract: In search of a vindication for the privileged position of a binary composition operation, one might well be led to consider a general $n$-place composition operation. An immediate concern is how to generalise the notion of associativity to this setting. This talk provides an explicit axiomatisation of categories with an $n$-place associative tensor product structure, tentatively called $n$-associative categories, utilising a generalisation of the Mac Lane-Stasheff pentagon axiom and one new class of hexagon axioms. We also sketch a proof of a coherence theorem for such a structure, showing that each $n$-associative category is equivalent to one canonically generated by a $2$-associative category.
I'll be back in Canberra around Sept 16 to go to a concert with elfishski and (probably) give at least one talk on my current research. On the flip side, Canberrans (or other non-Sydneysiders) who want to come up to Sydney to see a concert or such, will soon have a sleeper couch on which to rest their tired heads.
The week after that is the AustMS conference, conveniently located this year at Macquarie. This will be my third year in a row going to this conference - it's fast becoming one of the events I look forward to each year. Anyone else going?
I have also started trying to learn Russian. anya_1984 eventually managed to convince me that there is a difference in the way you pronounce ш and щ. I think that I can even vaguely pronounce them correctly. I guess this is a start at least...
I'll be speaking in the category theory special session. I'll probably be hanging out there and in the combinatorics and group theory special sessions for the most part.
Title: Associative categories
Abstract: In search of a vindication for the privileged position of a binary composition operation, one might well be led to consider a general $n$-place composition operation. An immediate concern is how to generalise the notion of associativity to this setting. This talk provides an explicit axiomatisation of categories with an $n$-place associative tensor product structure, tentatively called $n$-associative categories, utilising a generalisation of the Mac Lane-Stasheff pentagon axiom and one new class of hexagon axioms. We also sketch a proof of a coherence theorem for such a structure, showing that each $n$-associative category is equivalent to one canonically generated by a $2$-associative category.