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May
12
answered Categorical Foundations text
Apr
21
comment Comparing Category Theory and Model Theory for Master's Thesis.
Here are two references to applications of category theory: n category cafe link talks about many areas of applications with emphasis on physics. David Spivak, Category theory for the sciences link emphasizes applications to database theory, which has suddenly become a big deal among data base people.
Apr
21
comment Comparing Category Theory and Model Theory for Master's Thesis.
Here is a start on references to applications of category theory:
Mar
20
answered Set notation for generalized elements
Mar
2
answered Is it possible to construct ZFC set theory inside category theory?
Apr
29
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
I discovered a special case of this in third (?) grade: 3 times 37 is 111. It caught my attention -- how could THAT happen?
Apr
10
comment Closing up the elementary functions under integration
I don't know what you mean by "elementary integral". If you mean "if the integral f of a given elementary function g is also elementary, is f elementary? The answer is no: e^(x^2) is the integral of the function 2x e^(x^2), but e^(x^2) is not elementary.
Jul
24
comment How to check whether it is a direct product?
If you are given the operation (A,B)↦A×B, then a product preserving functor between categories with finite products must preserve the specified product. If you require only that there be an object A times B with the required properties, then a product preserving functor must take a product to SOME product of the images of A and B (of course, they are all naturally isomorphic). Note: This is a fine point that hardly ever makes any difference in practice! See Toposes, Triples and Theories at www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf, page 141.
Jun
29
awarded  Yearling
May
20
awarded  Good Answer
Nov
14
awarded  Nice Question
Oct
20
awarded  Nice Answer
Aug
22
awarded  Teacher
Aug
22
asked Closing up the elementary functions under integration
Aug
22
answered Which one result in mathematics has surprised you the most?
Aug
22
answered Which one result in mathematics has surprised you the most?
Aug
14
awarded  Supporter
Aug
14
comment Has L'Hopital's Rule been studied as an operator?
@George S. I meant that it has an orbit of length 2 in its action on whatever it is acting on, which at this point I am not sure of!
Aug
14
awarded  Editor
Aug
14
comment Has L'Hopital's Rule been studied as an operator?
@KennyTM You are right. I edited the question to reflect this.