Hi Jon, List, Thank you for sending the links--especially to the discussion. It is helpful--and quite funny.
For those who are a new to category theory, the explanation provided in the Stanford Encyclopedia of philosophy is a pretty good place to start. The section on the history of category theory provides context that is helpful for seeing where the two works by Mac Lane, Lambeck and Scott that Jon refers us to fit into the larger story. The bibliography is fairly comprehensive. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jon Awbrey [[email protected]] Sent: Tuesday, April 29, 2014 12:40 PM To: Jeffrey Brian Downard Cc: Peirce List Subject: Re: category theory in math Peircers, Category theory, along with its applications to logic and computation, has been a recurrent subject of discussion in many online groups over the last 15 years or so, just since I came online, anyway. Here are excerpts from basic texts that served as springboards and resources for these groups, along with a few bits of associated commentary and discussion, that I archived at the InterSciWiki site. Perhaps a few readers on the Peirce will find these of use by way of informing their discussions. Excerpts from Saunders Mac Lane (1971/1997), ''Categories for the Working Mathematician'' ========================================================================================= ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#CAT._Category_Theory ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#CAT._Category_Theory_.E2.80.A2_Discussion Excerpts from J. Lambek and P.J. Scott (1986), ''Introduction To Higher Order Categorical Logic'' ================================================================================================= ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#HOC._Higher_Order_Categorical_Logic ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#HOC._Higher_Order_Categorical_Logic_.E2.80.A2_Discussion Regards, Jon Jeffrey Brian Downard wrote: > Jerry, List, > > We might add that category theory, as it has been developed in mathematics in > the 20th century, is a generalization upon the conception of a mathematical > group. Peirce was quite familiar with Klein's use of group structure as a > basis for exploring the relations between different areas of mathematics. As > such, we should not assume that the general idea of what is involved in the > conception of mathematical category is entirely foreign to Peirce. > > Jeff > > > Jeff Downard > Associate Professor > Department of Philosophy > NAU > (o) 523-8354 -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ isw: http://intersci.ss.uci.edu/wiki/index.php/JLA oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache
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