I have written a short article with my response on Todd Trimble’s commentary on my book.

In this response I present these of Todd Trimble’s results which are new for me.

Note that I skipped specifically category-theoretic results (such as that the category of endofuncoids is topological). I am going to amend my article with categorical results later.

Todd Trimble has notified me that he has written a “commentary” (notes) on my theory of funcoids presented in my monograph.

His commentary is available at this nLab wiki page.

I’ve started to read his notes. First I needed to lookup into Wikipedia to know what Chu space is. He uses category theory however as it now seems to me not very advanced. So I hope to understand his writing in soon time.

**Conjecture** For every funcoid and filter , :

- ;
- .

**Conjecture** for every reloid .

**Conjecture** for every funcoid .

(I use notation from this note and this draft article.)

I have recently proved that there is an order isomorphism between funcoids and filters on the lattice of finite unions of Cartesian products of sets.

Today I’ve proved that this bijection preserves composition.

See this note (updated) for the proofs.

I have just proven the following two new theorems:

**Theorem** Composition of complete reloids is complete.

**Theorem** if and are both complete funcoids (or both co-complete).

See this note for the proofs.

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