Abstract We prove a strictification theorem for cartesian closed bicategories. First, we adapt Power’s proof of coherence bicategories with finite bilimits to show that every bicategory bicategorical structure is biequivalent 2-category 2-categorical structure. Then how extend this result Mac Lane-style “all pasting diagrams commute” theorem: precisely, in the free on graph, there at most one 2...

The localization game is played by two players: a Cop with team of k cops, and Robber. initialized the Robber choosing vertex r∈V, unknown to Cop. Thereafter, proceeds turn based. At start each turn, probes vertices in return receives distance vector. If can determine exact location r from vector, located wins. Otherwise, allowed either stay at r, or move r′ neighbourhood r. then again vertices...

DP-coloring (also called correspondence coloring) is a generalization of list coloring introduced by Dvo\v{r}\'{a}k and Postle in 2015. Motivated results related to Cartesian products graphs, we initiate the study DP-chromatic number, $\chi_{DP}$, same. We show that $\chi_{DP}(G \square H) \leq \text{min}\{\chi_{DP}(G) + \text{col}(H), \chi_{DP}(H) \text{col}(G) \} - 1$ where $\text{col}(H)$ nu...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...