This is a very interesting paper devoted to studying the relationship between two well-known concepts of filters in the context of lattice-valued spaces: $\top$-filters and stratified $L$-filters. \par In [Iran. J. Fuzzy Syst. {\bf 14} (2017), no.~3, 121--138, 188; MR3699810] Q. Yu and J.~M. Fang introduced the so-called category of $\top$-convergence spaces based on the following notion of $\top$-filter due to U. Höhle [Manuscripta Math. {\bf 38} (1982), no.~3, 289--323; MR0667918]: \par Definition. Let $L$ be a complete Heyting algebra and $X$ be a set. A nonempty subset $\germ{F}\subseteq L^X$ is called a $\top$-filter if: \roster \item"$\bullet$" $\bigvee_{x\in X} a(x)=\top$ for every $a\in\germ{F}(X)$; \item"$\bullet$" if $a,b\in\germ{F}$ then $a\wedge b\in\germ{F}$; \item"$\bullet$" given $d\in L^X$, if $\bigvee_{a\in\germ{F}} \bigwedge_{x\in S}a(x)\to d(x)=\top$ then $d\in\germ{F}$, \endroster where $\to$ is the right adjoint of the operation $x\wedge - $. \par The family of all $\top$-filters on $X$ is denoted by $\germ{F}_L^\top (X)$. \par The category $\top$-${\bf Conv}$ of $\top$-convergence spaces has as objects the following spaces: \par Definition. Let $L$ be a complete Heyting algebra. A $\top$-convergence space is a pair $(X,q)$ where $X$ is a nonempty set and $q\:\germ{F}_L^\top (X)\to 2^X$ satisfies: \roster \item"$\bullet$" $x\in q([x])$ for all $x\in X$, where $[x]=\{a\in L^X\:a(x)=\top\}$; \item"$\bullet$" if $x\in q(\germ{F})$ and $\germ{F}\subseteq \germ{G}$ then $x\in q(\germ{G})$. \endroster \par For its part, the stratified $L$-filters are defined as follows [U. Höhle and A.~P. Šostak, in {\it Mathematics of fuzzy sets}, 123--272, Handb. Fuzzy Sets Ser., 3, Kluwer Acad. Publ., Boston, MA, 1999; MR1788903]: \par Definition. Let $X$ be a nonempty set. A map $\nu\:L^X\to L$ is called a stratified $L$-filter if $\nu$ satisfies the following properties: \roster \item"$\bullet$" $\nu(1_\varnothing)=\bot$ and $\nu(\alpha 1_X)\geq \alpha$, where $\alpha\in L$; \item"$\bullet$" if $a\leq b$ then $\nu(a)\leq \nu(b)$; \item"$\bullet$" $\nu(a)\wedge\nu(b)\leq\nu(a\wedge b)$. \endroster The family of all $\top$-filters on $X$ is denoted by $\germ{F}^S_L (X)$. \par The above filters give rise to the following kind of convergence spaces [G. Jäger, Fuzzy Sets and Systems {\bf 282} (2016), 62--73; MR3413483]: \par Definition. Let $L$ be a complete Heyting algebra. A stratified convergence space is a pair $(X,\overline{q})$ where $X$ is a nonempty set, $\overline{q}=(q_\alpha)_{\alpha\in L}$ and $q_\alpha\:\germ{F}_L^S (X)\to 2^X$ satisfies: \roster \item"$\bullet$" $x\in q_\alpha (\langle x\rangle)$ for every $x\in X$, where $\langle x\rangle (a)=a(x)$ for every $a\in L^X$; \item"$\bullet$" $x\in q_\bot (\nu_\bot)$ for every $x\in X$, where $\nu_\bot (a)=\bigwedge_{x\in X} a(x)$ for every $a\in L^X$; \item"$\bullet$" if $\nu\leq \mu$ and $x\in q_\alpha(\nu)$ then $x\in q_\alpha (\mu)$; \item"$\bullet$" if $x\in q_\beta(\mu)$ and $\alpha\leq \beta$ then $x\in q_\alpha(\mu)$. \endroster \par The category $SL$-${\rm CS}$ has as objects the stratified $L$-convergence spaces. \par Then the authors prove that $\top$-${\bf Conv}$ is a bicoreflective subcategory of $SL$-${\rm CS}$ and if $L$ is also a Boolean algebra then it is a bireflective subcategory. \par Moreover, the authors also provide a characterization of the concept of regularity of $\top$-filters as introduced in [Q. Yu and J.~M. Fang, op. cit.] by means of the convergence of the closure of a $\top$-filter. Also, it is shown that a $\top$-convergence space is topological in the category $\top$-${\bf Conv}$ if and only if its image under the embedding of $\top$-${\bf Conv}$ into $SL$-${\rm CS}$ also is topological in this category. Finally, the authors also construct a compactification of a $\top$-convergence space when $L$ is a complete Boolean algebra.