Subject: Terminology for Kan extensions

From: categories <[email-masked]>
Date: Wed, 28 Jan 1998 10:22:45 -0400 (AST)

Date: Wed, 28 Jan 1998 10:25:34 +0000 (GMT)
From: Ronnie Brown <[email-masked]>

There seems some confusion as to whether Left Kan extensions are right 
Kan extensions and conversely, and it seems different authors use 
different conventions. 

What do people think of using a terminology analogous to limits and 
colimits, i.e. Kan extensions and Kan coextensions? In particular, what 
Carmody and Walters call left Kan extensions would here be Kan 
coextensions, which can be constructed as coends (as in Mac Lane, CFTWM). 

This point has come from Anne Heyworth, where left Kan extensions use 
right rewriting, if you write composition in a category in the algebraic 
rather than functional way. 

Any other ideas? 

Ronnie

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