O'Reilly logo

Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

ARTICLE VII

images

The Connected Components Functor

1.  Connectedness versus discreteness

Besides map spaces and the truth space, another construction that is characterized by a ‘higher universal mapping property’ objectifies the counting of connected components. Reflexive graphs and discrete dynamical systems, though very different categories, support this ‘same’ construction. For example, we say that dots d and d′ in a reflexive graph are connected if for some n images 0 there are

dots d = d0, d1.,…, dn = d′ and

arrows a1,…, an such that

for each i either ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required