Reports of the Midwest Category Seminar IV

Cover......Page 1
Title Page......Page 3
Table of Contents......Page 5
Terminology......Page 7
1. Introduction......Page 10
2. Induced Natural Transformations......Page 11
3. Premonoidal Categories......Page 23
4. Monoidal Categories......Page 32
5. Other Examples......Page 38
References......Page 44
Introduction......Page 45
1. Relations......Page 46
2. Relational Algebras......Page 49
3. Topological spaces......Page 54
4. Other examples......Page 59
References......Page 61
0. Introduction......Page 62
1. The Machine......Page 65
2. Behavior in the Limit......Page 80
(i) Categories of fractions......Page 85
(ii) M-objects......Page 90
(iii) Completions......Page 97
References......Page 105
The Right Adjoints into the Categories of Relational Systems......Page 106
1. Preliminaries......Page 107
2. Universal adjunctions for relational theories......Page 111
3. Right adjoints into categories of relational systems and other consequences......Page 114
References......Page 119
Triads in the Homology of Categories......Page 120
1. André homology [1]......Page 121
2. Barr and Beck homology [2]......Page 122
3. Adjoint functors......Page 123
4. Proof of the theorem......Page 127
References......Page 131
Dinatural Transformations......Page 132
References......Page 143
Categorically, the Final Examination for the Summer Institute at Bowdoin College (Maine) 1969......Page 144