This is an announcement for the paper "Tightness of Banach spaces and Baire category" by Valentin Ferenczi and Gilles Godefroy. Abstract: We prove several dichotomies on linear embeddings between Banach spaces. Given an arbitrary Banach space X with a basis, we show that the relations of isomorphism and bi-embedding are meager or co-meager on the Polish set of block-subspaces of X. We relate this result with tightness and minimality of Banach spaces. Examples and open questions are provided. Archive classification: math.FA Mathematics Subject Classification: 46B20, 54E52 Remarks: 13 pages Submitted from: ferenczi@ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.6444 or http://arXiv.org/abs/1111.6444