Category Theory as Coherently Constructive Lattice Theory (1998).pdf

文档介绍：Category Theory
as
Coheren tly Constructiv e Lattice Theory
W orking Do cumen t
Roland Bac khouse
Marcel Bijsterv eld
Rik v an Geldrop and Jaap v an der W oude
June
Con ten ts
In tro duction

Basic De
nitions

Categories

Initial Ob jects

F unctors


Natural T ransformations

Examples of Categories

Discrete Category


Opp osite Category

Category of Categories


F unctor Category

Sum Category

Elemen tary Illustrations

The Initial F unctor

Y oneda
s Lemma


In Lattice Theory

The Ev aluation F unctor


Hom F unctors
Generalised

The Lemma

Corollaries

Adjunctions

Galois Connections


Examples

In tro duction and Elimination Rules

P oin t wise Ordering of F unctions


Prop erties

Suprema

P arameterised Suprema


De
nition

Prop erties
Category Theory i June
ii

Sharp and Flat

Limits and Colimits

P arameterised Colimit