functors videos

Slice and comma categories 1

Duracion: 9:43
Votos: 5.00 from 4 people
Reproducciones: 275' favoriteCount='1
Autor: TheCatsters

Tags: category comma functor produce pullback slice

Definition of slice categories C/X and X/C, products in C/X as pullbacks in C

Adjunctions from morphisms 2

Duracion: 9:31
Votos: 5.00 from 4 people
Reproducciones: 204' favoriteCount='2
Autor: TheCatsters

Tags: bundles category fibration sets slice

The category of bundles on a set as a slice category and as a functor category into sets.

Adjunctions from morphisms 1

Duracion: 8:7
Votos: 5.00 from 5 people
Reproducciones: 352' favoriteCount='1
Autor: TheCatsters

Tags: grothendieck's operations pull-back push-forward six

Motivation for the construction of adjoint functors for bundles over sets

Metric spaces and enriched categories 2

Duracion: 10:24
Votos: 4.50 from 6 people
Reproducciones: 1335
Autor: TheCatsters

Tags: category enriched metric space V-functor

The definition of a generalized metric space as an enriched category. The definition of a metric map as an enriched functor.

Monoid objects 2

Duracion: 6:39
Votos: 5.00 from 5 people
Reproducciones: 363' favoriteCount='1
Autor: TheCatsters

Tags: category commutative Eckmann functor Hilton monoid

A monoid object in the category of monoids is a commutative monoid. We use the Eckmann-Hilton argument.

Monoid objects 1

Duracion: 8:28
Votos: 5.00 from 7 people
Reproducciones: 616
Autor: TheCatsters

Tags: categories functions functors internal monoids sets

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.

Eckmann-Hilton 1

Duracion: 8:50
Votos: 5.00 from 4 people
Reproducciones: 457' favoriteCount='1
Autor: TheCatsters

Tags: category commutative Eckmann functor Hilton

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".