Date: Fri, 8 Jan 1999 10:01:22 -0800
From: Eva SCHLAEPFER <esch@math.mcgill.ca>
Subject: categories: References

Hello,

can someone give me references for the following two constructions?

- in a closed monoidal category, the multiplication on the inner hom is
normally defined as the transpose of 

B tens (B -o B) tens (B -o B) ---> B tens (B -o B) ---> B

where tens is the tensor product, -o the inner hom, the first map ev tens
(B-o B) and the second ev.

- A,B,C objects in a monoidal category and A is a monoid. 
If B is an A-right-module in the sense that there is a morphism 
f: B tens A ---> B which satisfies certain axioms and C is a
A-left-module g:A tens C ---> C, then the quotient B tens_A C can be
defined as the coequalizer of the two
maps 
B tens g: B tens A tens C ---> B tens C   
and 
f tens C: B tens A tens C ---> B tens C

Thanks,

Eva Schlaepfer