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Representables and Yoneda 1
Representables and Yoneda 1
Definition of representable functors and the Yoneda embedding (though without calling it the Yoneda embedding yet) ... category functor representable yoneda
From:
TheCatsters
Views:
956
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Slice and comma categories 2
Slice and comma categories 2
Definition of comma categories D over and under F for a functor F, and F over and under G for functors F and G with the same target category ... category functor slice comma produce pullback [...]
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Monoid objects 1
Monoid objects 1
We define monoid objects in monoidal categories. We start with the motivating example of ordinary monoids, re-expressing it using only the objects and morphisms in the category Set. ... categories functors monoids internal sets functions
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Double categories
Double categories
Definition of double categories as internal categories in Cat, and brief unravelling of this definition ... categories functors double internal
From:
TheCatsters
Views:
741
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2-categories 2
2-categories 2
The middle four interchange law in a 2-category comes from functoriality of the composition functor. ... categories functors 2-categories interchange
From:
TheCatsters
Views:
717
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Outtakes (Catsters 35)
Outtakes (Catsters 35)
Happy New Year. [It's disturbingly similar to uk.youtube.com ... categories functors outtakes
From:
TheCatsters
Views:
1645
13
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Distributive laws 3 and/or Monads 6 [29]
Distributive laws 3 and/or Monads 6 [29]
We introduce the idea of monads *in* a general 2-category C (where putting C = Cat gives the usual notion of monad *on* a category), and define the 2-category Mnd(C) of monads, monad functors and [...]
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String diagrams 1
String diagrams 1
A first look at the string diagram notation for representing categories, functors and natural transformations. ... category functor natural transformation string diagram
From:
TheCatsters
Views:
3958
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Monads 3
Monads 3
The definition of algebras for monads. The example of monoids as algebras for the monoid monad. ... functors categories monads monoids algebras
From:
TheCatsters
Views:
2853
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Finite Simple Group (of Order Two)
Finite Simple Group (of Order Two)
From my domain, its image looks so blue, 'Cause all I see are zeroes, it's a cruel trap But we're a finite simple group of order two I'm not the smoothest operator in my class, But [...]
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