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## Decomposition of completions of reloids ★★

Author(s): Porton

**Conjecture**For composable reloids and it holds

- \item if is a co-complete reloid; \item if is a complete reloid; \item ; \item ; \item .

Keywords: co-completion; completion; reloid

## A construction of direct product in the category of continuous maps between endo-funcoids ★★★

Author(s): Porton

Consider the category of (proximally) continuous maps (entirely defined monovalued functions) between endo-funcoids.

Remind from my book that morphisms of this category are defined by the formula (here and below by abuse of notation I equate functions with corresponding principal funcoids).

Let are endofuncoids,

We define

(here and are cartesian projections).

**Conjecture**The above defines categorical direct product (in the above mentioned category, with products of morphisms the same as in

**Set**).

Keywords: categorical product; direct product

## List Total Colouring Conjecture ★★

Author(s): Borodin; Kostochka; Woodall

**Conjecture**If is the total graph of a multigraph, then .

Keywords: list coloring; Total coloring; total graphs