Posina Venkata Rayudu’s Reviews > Conceptual Mathematics: A First Introduction to Categories > Status Update

I want to understand: form a cohesive body of thought by putting together those pieces of my knowledge that fit together.

If S, d, c is a given bipointed object in a category, then for each object X of the category, the graph of 'X fields' on S is a reflexive graph, and for each morphism f: X –> Y, the induced maps on sets constitute a morphism of reflexive graphs.
http://namingthegiven.wordpress.com/2...

If x is connected to y and y is connected to z, then x is connected to z.

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On forgetting and imagining

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One thing that always struck me was Bill Lawvere's observation that the dual of the usual definition of function as a subset of a product s.t.... namely as a quotient of a sum s.t.... actually corresponds closely to the usual picture we draw when we introduce functions for the first time.
Michael Barr
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Conscious Experience is / is not determined by Neural Coding

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The Connected Components Functor
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If you look at the distributive law

A x (B + C) = (A x B) + (A x C)

and see rectangles, what, then, is wrong with looking at

A + (B x C) = (A + B) x (A + C)

and asking for a corresponding image–may be not rectangles flashing area, may be one of those impossible visions (of climbing Penrose staircase)...

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An ancient principle of mathematics holds that a figure is the locus of a varying element. The varying element, as a single thing, is a single figure or element itself.
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How Russell made paradox out of Cantor's theorem?
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