A wide array of syntactic phenomena can be categorized as being either direction-sensitive (e.g. coordination) or direction-insensitive (quantification and medial extraction). In the realm of categorial grammar, many frameworks are engineered to handle one class of phenomena at the expense of the other. In particular, Lambek-inspired frameworks handle direction-sensitivity elegantly but struggle with cases of direction-insensitivity, whereas in linear grammars, the situation is just the opposite. One reasonably successful attempt to unify the insights of both types of grammar and allow (...) for the analysis of direction-sensitive as well as direction-insensitive phenomena is hybrid type-logical categorial grammar (HTLCG), which augments the set of syntactic categories of an ordinary linear grammar with the directional slashes of a Lambek grammar. In this paper, the complementary nature of Lambek and linear grammars, with respect to direction-sensitive and direction-insensitive phenomena, is expounded on, as is the nature of how HTLCG attempts to reconcile the two systems. The paper further discusses an alternative to HTLCG—a linear grammar which adds Lambek-like capabilities by augmenting the string-combining (phenogrammatic) mechanism instead of the definition of syntactic categories (the tectogrammar). In particular, LCGϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {LCG}_\phi $$\end{document} (linear categorial grammar with phenominators) adds a form of subtyping based on phenominators—a class of linear functions which specify various modes of (phenogrammatic) combination. Most importantly, an algorithm is provided for embedding HTLCG into LCGϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {LCG}_\phi $$\end{document}, thereby demonstrating that LCGϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {LCG}_\phi $$\end{document} can handle direction-(in)sensitivity at least as well as HTLCG. (shrink)