The YELLOW series

Recall that the articles in the YELLOW series are intended to cover the background material assumed by the CCL-book. This series of 22 articles (out of 57 total in the project) indicates that MML was in considerably good shape for the formalization (see some numbers in Section ). However, in order to fill the gap, the following topics had to be developed.

• Relational structures

  $\bullet$ substructures: YELLOW_0, YELLOW_2, YELLOW_6 $\bullet$ products: YELLOW_1, YELLOW_3, YELLOW10 $\bullet$ bounds: YELLOW_0, YELLOW_5 $\bullet$ duality: YELLOW_7 $\bullet$ isomorphism: YELLOW14.

• Posets

  $\bullet$ bounds, suprema and infima: YELLOW_0 $\bullet$ Boolean posets: YELLOW_1 $\bullet$ retracts: YELLOW16.

• Lattices

  $\bullet$ complete: YELLOW_0, YELLOW_2 $\bullet$ the lattice of ideals: YELLOW_2 $\bullet$ Boolean: YELLOW_2, YELLOW_5 $\bullet$ modular and distributive: YELLOW11 $\bullet$ lattice operations on subsets of a poset: YELLOW_4 $\bullet$ topological: YELLOW13.

• Topology

  $\bullet$ Moore-Smith convergence: YELLOW_6 $\bullet$ Baire and sober spaces: YELLOW_8 $\bullet$ bases: YELLOW_9, YELLOW13, YELLOW15 $\bullet$ augmentations and refinements: YELLOW_9 $\bullet$ Hausdorff spaces: YELLOW12 $\bullet$ products, Tichonov theorem: YELLOW14, YELLOW17 $\bullet$ retracts: YELLOW16 $\bullet$ compactness: YELLOW19.

• Category theory

  $\bullet$ concrete categories: YELLOW18 $\bullet$ isomorphisms, equivalence and duality: YELLOW18, YELLOW20, YELLOW21 $\bullet$ lattice-wise: YELLOW21.

In the following subsection, we discuss a number of these topics whose development raised some interesting issues.