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comment Is there any geometry where the triangle inquality fails?
In evolutionary game theory the Fisher information metric is called the Shahshahani metric. See "Evolutionary Game Theory" by Hofbauer and Sigmund. The information divergence can be used to give a Lyapunov function for the replicator equation. I believe this goes back to Akin; others use an exponentiated form (e.g. Hofbauer and Sigmund).
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answered Is there any geometry where the triangle inquality fails?
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awarded  Editor
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revised Homological Algebra for Commutative Monoids?
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Nov
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comment What is an intuitive view of adjoints? (version 1: category theory)
Just to emphasize on part of this response, note that an adjoint pair provides a global solution (category-wide) as opposed to a local solution provided by universal maps. So universality is more general, in that if the universal map exists for every object in the category, the family of universal maps can be used to define an adjoint.
Nov
23
comment Examples of mathematics motivated by technological considerations
Well it depends on what you mean by mathematical advance. If your metric is the creation of an entire new field, such as graph theory itself in this case, then I guess not.
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23
answered Examples of mathematics motivated by technological considerations
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awarded  Supporter
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answered Programming Languages based on Category Theory
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answered Relating Category Theory to Programming Language Theory
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answered Homological Algebra for Commutative Monoids?
Nov
17
comment How do I check if a functor has a (left/right) adjoint?
It's not all that hard to verify the definition directly in a lot of cases. Do you mean "not tedious"-to-check?
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17
answered How do I check if a functor has a (left/right) adjoint?
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awarded  Teacher
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answered How do you keep your research notes organized?