二重圏の一般化

昨日引用した↓

• Title: COMPOSITION OF MODULES FOR LAX FUNCTORS
• Author: ROBERT PARE
• URL: http://www.tac.mta.ca/tac/volumes/27/16/27-16.pdf
• Pages: 53p.

↑これは、weak double category の話が多い。

• Title: Tile Transition Systems as Structured Coalgebras
• Authors: Andrea Corradini, Reiko Heckel, Ugo Montanari
• URL: http://is.uni-paderborn.de/uploads/tx_sibibtex/Tile_Transition_Systems_Structured_Coalgebras.pdf

↑には、monoidal double categoryが出てくる。

以下の論文達は、double categoryも含む高次圏の話。

• Title: Intercategories
• Authors: Marco Grandis, Robert Paré
• URL: http://arxiv.org/abs/1412.0144

• Title: Intercategories: A framework for three-dimensional category theory
• Authors: Robert Paré, Marco Grandis
• URL: http://arxiv.org/abs/1412.0212

• Title: AN INTRODUCTION TO MULTIPLE CATEGORIES (ON WEAK AND LAX MULTIPLE CATEGORIES, I)
• Ahtors: MARCO GRANDIS AND ROBERT PARE
• URL: http://www.mscs.dal.ca/~pare/Mlc1.pdf
• Pages: 43p.

• Title: LIMITS IN MULTIPLE CATEGORIES (ON WEAK AND LAX MULTIPLE CATEGORIES, II)
• Authors: MARCO GRANDIS AND ROBERT PARE
• URL: http://www.mscs.dal.ca/~pare/Mlc2.pdf
• Pages: 29p.

↓はGarnerの学位論文。

• Title: POLYCATEGORIES
• Author: Richard H. G. Garner
• URL: http://comp.mq.edu.au/~rgarner/Thesis/Thesis.pdf

↑pseudo double categoryの話。

↓double bicategoryってのもある。

• Title: Double Bicategories and Double Cospans
• Author: Jeffrey C. Morton
• URL: http://arxiv.org/abs/math/0611930

↑チラッと読んだが、ここまでは不要な感じがした。

次のブログ記事もあった。

• Title: Bicategories, Pseudo Double Categories, and Double Bicategories
• URL: http://category.reluctantm.com/?p=40