ONT Re: Category Theory
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CAT. Discussion Note 2
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Links to the first three installments from Mac Lane are given below.
I am chunking this into small pieces specifically to facilitate the
group's discussion of content, formalism, motivation, or whatever.
In the 5 pages of his Introduction, Mac Lane is giving merely a
quick overview of some leading ideas and typical constructions,
so don't worry about the speed of it, as all of these things
will be gone back over in full detail, as time goes by.
For anybody who's up to a comparative study, all of the same basic notions
of category theory are covered from the standpoint of logical applications
in Lambek & Scott's 'Higher Order Categorical Logic', and there are links
to a sampling of that work below.
Jon Awbrey
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Category Theory
Introduction
01. http://suo.ieee.org/ontology/msg04463.html
02. http://suo.ieee.org/ontology/msg04466.html
03. http://suo.ieee.org/ontology/msg04467.html
The above material is excerpted from:
| Saunders Mac Lane,
|'Categories for the Working Mathematician',
| 2nd edition, Springer, New York, NY, 1997.
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Higher Order Categorical Logic
Part 0. Introduction to Category Theory
1. Categories and Functors
01. http://suo.ieee.org/ontology/msg03373.html
02. http://suo.ieee.org/ontology/msg03375.html
03. http://suo.ieee.org/ontology/msg03376.html
04. http://suo.ieee.org/ontology/msg03377.html
05. http://suo.ieee.org/ontology/msg03378.html
06. http://suo.ieee.org/ontology/msg03381.html
2. Natural Transformations
07. http://suo.ieee.org/ontology/msg03383.html
08. http://suo.ieee.org/ontology/msg03384.html
09. http://suo.ieee.org/ontology/msg03392.html
10. http://suo.ieee.org/ontology/msg03393.html
11. http://suo.ieee.org/ontology/msg03394.html
12. http://suo.ieee.org/ontology/msg03395.html
Part 1. Cartesian Closed Categories & Lambda Calculus
Introduction to Part 1
13. http://suo.ieee.org/ontology/msg03396.html
Historical Perspective on Part 1
14. http://suo.ieee.org/ontology/msg03398.html
15. http://suo.ieee.org/ontology/msg03399.html
16. http://suo.ieee.org/ontology/msg03400.html
17. http://suo.ieee.org/ontology/msg03401.html
18. http://suo.ieee.org/ontology/msg03402.html
1. Propositional Calculus as a Deductive System
19. http://suo.ieee.org/ontology/msg03403.html
20. http://suo.ieee.org/ontology/msg03404.html
21. http://suo.ieee.org/ontology/msg03405.html
22. http://suo.ieee.org/ontology/msg03406.html
2. The Deduction Theorem
23. http://suo.ieee.org/ontology/msg03409.html
3. Cartesian Closed Categories Equationally Presented
24. http://suo.ieee.org/ontology/msg03410.html
25. http://suo.ieee.org/ontology/msg03411.html
26. http://suo.ieee.org/ontology/msg03412.html
Back to Part 0
3. Adjoint Functors
27. http://suo.ieee.org/ontology/msg03415.html
28. http://suo.ieee.org/ontology/msg03416.html
29. http://suo.ieee.org/ontology/msg03417.html
30. http://suo.ieee.org/ontology/msg03418.html
The above material is excerpted from:
| Lambek, J. & Scott, P.J.,
|'Introduction To Higher Order Categorical Logic',
| Cambridge University Press, Cambridge, UK, 1986.
|
| http://uk.cambridge.org/mathematics/catalogue/0521356539/
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