Skip to content
November 26, 2016 / porton

A new diagram about funcoids and reloids

Define for posets with order \sqsubseteq:

  1. \Phi_{\ast} f = \lambda b \in \mathfrak{B}: \bigsqcup \{ x \in \mathfrak{A} \mid f x \sqsubseteq b \};
  2. \Phi^{\ast} f = \lambda b \in \mathfrak{A}: \bigsqcap \{ x \in \mathfrak{B} \mid f x \sqsupseteq b \}.

Note that the above is a generalization of monotone Galois connections (with \max and \min replaced with suprema and infima).

Then we get the following diagram (see this PDF file for a proof):


It is yet unknown what will happen if we keep apply \Phi_{\ast} and/or \Phi^{\ast} to the node “other”. Will this lead to a finite or infinite set?


One Comment

Leave a Comment
  1. porton / Nov 26 2016 20:11

    The diagram was with an error. I have edited the post.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: