[FONT=“Comic Sans MS”][COLOR="#300090"]TropicFlower,
How to emulate a knitting YO (K-YO) in crochet depends on what you want to do. In knitting the YO increase creates a hole in the fabric that is useful for lace work as well as increasing the length of the next row. I think I have also seen it used to create an [B][U][COLOR=“Blue”]elongated knit stitch[/COLOR][/U][/B], for a tall, open, and lace like row.
Both KnittinMitchie and MathWizard are correct depending on what you want to do. You mentioned doilies, lace, and filet; but you didn’t say if your pattern is in-the-round or rectangular. That makes a big difference in what type of increase you want and where to put it.
If your working in the round like a lace doily, then use a chain to duplicate each knitting YO (K-YO). On the next round you can either crochet into the chain or around/under them (go under the chain to pick up your loop for your next stitch). Since this is an internal increase it makes the next row longer and causes the fabric to bend. That is ideal for working in the round were each new round must be six, seven, or eight stitches longer than the previous round to keep the work flat.
If your pattern is rectangular, making rows back and forth, then you could use the chain to replace the K-YO if you also skip a stitch of the previous row (like filet). That wouldn’t be an increase. If you do need to increase then do that at the ends of the rows like MathWizard suggested.
If the YO created a corner in the Knit fabric, like a lacy diagonal (raglan style) seam with a sleeve, then you would use three chains to replace the K-YO. Three creates a corner. If you combine a decrease before turning the corner I would suggest just two chains. If it will be an inside corner, like the bottom of a V, then it is a two stitch decrease with a skip between.
If the K-YO was used to create an extra tall, lacy row in the knit fabric, then you would replace with a treble crochet or larger. Or you could [COLOR=“Blue”][U][B]extend the stitches[/B][/U][/COLOR] with one or more chains in the loop you pulled up/through from the previous row.
{I’ll be back in a moment with a link to [U][COLOR=“blue”][B]some crochet stitch instructions[/B][/COLOR][/U], just as soon as I find them.}
–Jack[/COLOR][/FONT]