Distributive laws 4  Distributive laws as monads in the 2-category Mnd(C).
String diagrams 4 Monads in the string diagram notation. The unit and associativity identities as topological moves.
Adjunctions 4 The two notions of adjunction coincide.
Joseph Johnson - Unstable Homotopy Theory Conference 2009 "Lambda-rings and a functor K(X)" In this talk I will discuss lambda-rings and a functor K(X), which is a direct sum of certain G-equivariant K-theory groups. Speciﬁcally, I will demonstrate a lambda-ring structure on it and share some thoughts I have had recently.
Adjunctions 7 The adjunction coming from the Kleisli category. The category of adjunctions for a monad: the Eilenberg-Moore and Kleisli categories as terminal and initial objects.
Monads 3A An appendix to Monads 3: more on monoids as algebras for the monoid monad.
Monoid objects 2 A monoid object in the category of monoids is a commutative monoid. We use the Eckmann-Hilton argument.
Natural transformations 3 The interchange law for horizontal and vertical composition, "proof" using whiskering. This video is a bit quiet and a bit fuzzy and we'll probably replace it with an improved version soon.
Distributive laws 2 The key result about how a distributive law of S over T gives relationships between S-algebras, T-algebras and TS-algebras.
Adjunctions 3 Adjunctions give rise to monads.
Monads 2 Continuation of the monoid monad example and introduction of the category monad.
String diagrams 5 Adjunctions give rise to monads.
Natural transformations 1 The definition of natural transformations. An ***ogy with homotopy.
Eckmann-Hilton 1 We present and prove the Eckmann-Hilton argument: given a set with two binary, unital operations that distribute over one another, in fact the two operations must be the same and commutative. Proved using the Eckmann-Hilton "clock".
Adjunctions 1 The notion of an adjunction. Definition via unit and counit natural transformations and the triangle identities.
Representables and Yoneda 2 Further explanation of the Yoneda embedding (including calling it that, but not yet proving it's an embedding), checking naturality for H_f.
Slice and comma categories 1 Definition of slice categories C/X and X/C, products in C/X as pullbacks in C
String diagrams 2 The interchange law and whiskering. The last dull bits before getting onto adjunctions. (Apologies for the drastic editing at the end.)
Adjunctions 5 Every monad comes from an adjunction via its category of algebras.
String diagrams 3 The definition of adjunctions in string diagram language - the snake/zig-zag relation.
Natural transformations 2 More on natural transformations: vertical and horizontal composition.
Metric spaces and enriched categories 2 The definition of a generalized metric space as an enriched category. The definition of a metric map as an enriched functor.
The Coherence Incubator - Overview An Overview of The Coherence Incubator including a description of what is the Incubator is, reasons to use it and a brief description of each of the current projects: The Patterns: Coherence Common The Command Pattern The Functor Pattern The Messaging Pattern The Push Replication Pattern The Processing Pattern
Adjunctions 6 Definition of the Kleisli category
The Ode | Edwin Stolk | 2010 Never seek power--only release it. The Ode | 2010 is one of the acts out of undefined more acts and connected with and grown out of situation: The hanging gardens of Babylon | 2010. The hanging gardens of Babylon is a subjective and ambiguous situation in the Noord-Holland dune area, doomed to vanish. As part of temporary museum Heemskerk. You can be part of ; The hanging gardens of Babylon, till 26 September 2010. (English) (Dutch) www.schone- (Sorry Dutch only) Drop YOUR text version about the situation at the situation pay desk or under the video below, thanks a lot! More?
Functor | Edwin Stolk | 2010 Functor | 2010 is one of the first acts out of undefined more acts and connected with and grown out: The hanging gardens of Babylon | 2010. The hanging gardens of Babylon is a subjective and ambiguous situation in the Noord-Holland dune area, doomed to vanish. As part of temporary museum Heemskerk. You can be part of ; The hanging gardens of Babylon, till 26 September 2010. www.schone- (Sorry Dutch only) Drop YOUR text version about the work at the situation pay desk or under the video below, thanks a lot!
Adjunctions 2 Definition of adjunction via natural isomorphism between hom-sets. Getting the unit and counit from this.
String diagrams 1 A first look at the string diagram notation for representing categories, functors and natural transformations.
2-categories 2 The middle four interchange law in a 2-category comes from functoriality of the composition functor.
Natural transformations 3A Addendum to natural transformations 3: a bit more about whiskering, and where the interchange law really comes from
Monads 1 An introduction to monads including the definition and a look at the monoid monad.
Representables and Yoneda 1 Definition of representable functors and the Yoneda embedding (though without calling it the Yoneda embedding yet)
Distributive laws 1 Definition of distributive law of one monad over another, and the example of multiplication distributing over addition.
Monads 4 Morphisms between algebras and the category of algebras. A first look at the question of monadicity.
Representables and Yoneda 3 Statement of Yoneda lemma and explanation of "why" it is true
Truecombat Community Movie A little something I put together that features some of the best players to ever play truecombat. All frags and caps are from TCL season 4 and 5 and TCUCL Invitational.
Distributive laws 3 and/or Monads 6  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 monad transformations in C as in Street, The formal theory of monads.
Monads 3 The definition of algebras for monads. The example of monoids as algebras for the monoid monad.
Adjunctions from morphisms 2 The category of bundles on a set as a slice category and as a functor category into sets.